Find the approximate derivative for f(x) = cos x on the interval [-7, 1] using forward difference formula with step size h = . Find exact derivative and approximate derivative values and compute absolute error.

Q: y = sin(0.5 Vx)/x at x = 1, h = 0.2

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Q: Find the critical numbers of the function and apply the First Derivative Test to identify all…

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Q: Using the Backward, F

A: Given,               f(x)=-0.5x5+0.18x4-1.2x3+0.8x2-2.3 and x=0.25, h=0.05

Q: Find the derivative of f(x) = tan tan (3x2+2x)( Ans: (6x + 2) sec2 (3x2+2x) solution?

A: Let,

Q: Find the Equation of tangent line of the function f(x)=1+csc(x)-√cos(x) at the point…

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Q: Solve for the derivative of the function using chain rule. 9. f(x)= esinx

A: Solve for the derivative of the function using chain rule. 9. f(x)= esinx

Q: Find the derivative of the given function. Infsech(x) + tanh(x)) 1) sechx+tanhr sinhx+1 sechx-tanhx…

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Q: HiHtar is THe secoyd derivative OF Y

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Q: Determine Step 3 using 4-Step Rule in finding the derivative of  y=2sin(x)cos(x).

A: Introduction: The four-step method to find derivatives is actually determining the derivative of a…

Q: Determine the second derivative of f (x)= x 'e* at x = -2 with a step-size of h=0.50 using Central…

A: We have to find the second derivative of the following function at x=-2 with step size h=0.5 using…

Q: Use central difference method to estimate the 1st derivative of the following function at x = 2 and…

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Q: Find the hundredth derivative of the function f (x) = cos(2x). O f(100) (x) = -2!00 cos(2x) O f(100)…

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Q: Find the derivative of the function using 3-step rule: v (t) = -.

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Q: What is the derivative of f(x)=3cos(x)+2sin(x) at the point x=−π

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Q: Find the critical points/number of the function h(x) = e^x sinx-sinx+cosx by applying derivatives.

A: First calculate its derivate then equate it equal to 0 to obtain the critical points. h(x)=exsin…

Q: Compute the required derivative approximations for the functions at the specified location, for the…

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Q: Consider the function f(x) = x³ – 2x + 4 on the interval (-2, 2) with h = 0.25. Use backward,…

A: Given that fx=x3−2x+4 To use backward, forward, and central difference methods to approximate first…

Q: Estimate the root very near x = 0.4 of 4(x*)" - 4(x²) + 1 = 0 using the Newton- Raphson Method with…

A: Consider a function:  fx=4xx4-4x2x+1      =4x4x-4x2x+1

Q: Compute the derivative using derivative rules that have been introduced so far y = cos4 θ

A: This question is taken from the derivative in which we have to find the derivative of the given…

Q: To investigate these values, we find the second derivative f"(x) = %3D At the positive critical…

A: Given function is : fx=3x-4x3

Q: Find the derivative ofƒ(x) = 1/x5in two different ways:using the Power Rule and using theQuotient…

A: given: f(x)=1x5 the differentiation of the function f(x)=1x5 by using the power rule is: the…

Q: Find the fourth derivative of f (z) = 2" + In (x) – 160z. %3D Enclose arguments of functions in…

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Q: fcx)= Y文 メ ー^

A: Local extrema

Q: Compute central difference approximations for the first derivative of the function, y = cos(sin(x)+…

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Q: 3. Find the derivative of f (x) tan (5x + 7), by first principle of differentiation

A: Given function is By first principle of differentiation, we have

Q: Use forward-difference formula to evaluate the first derivative of y = cos(x) at x = cos(x) at x =…

A: Given function is y=cosx. We have to evaluate the first derivative of y=cosx at x=π4 using a value…

Q: 1. Use forward, backward and central difference to estimate the first and second derivative of f (x)…

A: Given function is fx=coshx and x=2 Step size h=0.01 We have to estimate the first and second…

Q: Find a function with the given derivative whose graph passes through point P f'(x)= 2xx+1-cosx,…

A: To determine the antiderivative satisfying the given initial condition

Q: Find the derivative of the function. h(x) CoS x 6. %3D 1+ sin x sin x -61 coSX --6 cosx (1+ sin x)6…

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Q: h(x) = tan(x' sinx) sinx (b) y= - V1+ cosx

A: Topic = Derivative

Q: Compute the derivative of the function y = 8 sin-(x) at the point x = (Use symbolic notation and…

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Q: Use a central difference method to approximate the first derivative of cos(x) at x = pi/3., assume…

A: To approximate the first derivative of fx=cosx at x=π3 by taking the value of h=0.01.

Q: Apply central divided difference approximation (CDD) to find the first 5 derivative of F(x) = e0.8x…

A: To find the first five derivatives of fx=e0.8x when x=24 using central divided difference…

Q: Find all x values in interval [0,2 ·¤] on the graph of f(x) = -3·sin(x)·cos(x) where the tangent…

A: Given,            f(x) = -3 sin(x) cos(x)

Q: Find the derivative of the function using chain rule. f(x) = esin?x

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Q: Calculate first, second, and third derivative values for function, f(x) = -x2 + 5x + 3 at points x =…

A: Forward difference Consider a linear interpolation between the current data value (t0,I0) and the…

Q: We want to use the Richardson method to calculate the first order derivative antisymmetrically at…

A: We need atleast 2 points to calculate the Richardson second order derivative. The small parameter…

Q: Compute the derivative of the function y = 6 cos- (4x) at the point x = (Use symbolic notation and…

A: Solution ) y = 6 cos-14x Differentiate with respect to x  y' = 6 d/dx (cos-14x) [ we know that  d/dx…

Q: Solve for the derivative of the function using chain rule. 8. f(x)= sin (2x)cos (3x)

A: Given problem:- Solve for the derivative of the function using chain rule.   8.     f(x)= sin…

Q: Compute forward and backward difference approximations of O(h) and O(h2), and central difference…

A: Numerical differentiation includes three different types: forward difference, backward difference,…

Q: Solve for the derivative of the function using chain rule. 14. f(x)= 3lnx 15. f(x)= cos(cosx))

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Q: Determine the second derivative of f (x)=x²e* at x =-2 with a step-size of h=0.50 using Central…

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Q: Can the  derivative of f(x) be zero in the interval [-1,0]

A: Given, fx = x4+8x+3  f'x = 4x3+3   We have to find the derivative of fx be zero in the interval -1,0…

Q: 3. Estimate the derivative using forward finite divided difference applying both truncated and more…

A: Given f(x)=12+xe2x To find the f'0.5 at h1=0.25 and h2=0.125 using forward finite divided difference…

Q: Compute central difference approximations for the first derivative of the function, y = cos(sin(x)+…

A: here we will use central difference formula  f'x≈fx+∆x-fx-∆x2×∆x

Q: Find a function with the given derivative whose graph passes through point P f'(x)=1/x+2, x is…

A: The derivative is given as

Q: Using the đết of derivative, fin rivative of f(x) = x² + 2x + 2.

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Q: Find the critical numbers of the function and apply the First Derivative Test to identify all…

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Q: 2 12. f (x) = (1tsinx) Cosx

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Q: Find the derivative of the function y using the increment method or three- step rule. vx +1

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