Find the derivative of f(x) = arctan x In(6x? + 6x – 4) 1 1 -In(бx? + бх — 4) + arctan x- -(12x + 6) 1+x2 бх2+6х-4

Q: h(x)=(x° +1} (2x+5)*

A: Given : hx = x2+132x+52

Q: Compute the derivative of g(x)=arctan(x^3+1)

A: From the given data:

Q: Find the derivative using the chain rule: x(x^2+1)^(-1/2)

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Q: Find derivative of 2x^4y^3-xy^2 using chain rule.

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Q: 3. FIND THE DERIVATIVE BY THE LIMIT PROCESS OFf(x) = Vx+2.

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Q: 8. Find the derivative of f (x) = 2tanx – 3secx. Show all steps -

A: We have to find the derivative of the function fx=2tanx-3secx Then,…

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: What is the derivative of 1+x3 at the point (1, )? O 1/4 O- 1/4 O 1

A:

Q: Use the first principles delta method to find the derivative of y = x2 – x. %3D

A: Here we have to find the derivative of y by using the first principles delta method.

Q: Find the derivative. y= In x+3 %3D

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Q: Find the derivative of Ox²2cosx + 2xsin x O 2xcos x O x² sin x + 2xcos x O x2cosx y=x²sinx

A: We know that if f(x)=g(x)h(x) then  f'(x)=g'(x)h(x)+g(x)h'(x)

Q: find the derivative of f(x) = (x²+4)(3x³ - 2x) at the point x = - 3[ use product rule] %3D B.

A: We have to find the derivative

Q: 10. f(x) = cos (2x)e*²-1

A:

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: Use forward difference approximation to estimate the first derivative of the following equation.…

A: Given that, fx=-0.15x3-0.2x2-0.5x+2.25h=0.5We need to find the first derivative of the function at…

Q: 2) Find the derivative of the function f(x) = (x³ – tan(4x² – 2)* |

A: Given :            To find the derivative of the given function                f(x) = x3 -…

Q: if the derivative of x2sinx+2xcosx-sinx  is (Ax2+B)(cos(C(x/2))). FInd the value of A, B, and C.

A: Given: x2sinx+2xcosx-sinx Differentiate the equation.…

Q: (b) Use implicit differentiation by partial derivative to solve for of function 3x2 + 2xy = -4y3. dx

A:

Q: Give an example of a function f (x) that has one positive derivative on (−1,0) and a negative…

A:

Q: Find sixth order derivative of the function f(x)=(x-5)^7.cos(5x) by using Leibnitz theorem.

A: n! = n × (n-1) × (n-2) × (n-3) × (n-4) × ............ × 1

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

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Q: Choose the derivative of sin (x). - 1 1 1+ x2 1 x2 | 1 1+ x2 1 xVx2 1 - 1 V1- x?

A: It can easily find the derivative of function

Q: 5. Find the derivative of y = In(cos v3x + 2 ), by using chain Rule.

A:

Q: The derivative of the function y = etan(4x) is: a) y' = tan (4x)etan(4x) b) y' = 4 sec²(4x) etan(4x)…

A: Given data: The given function is y=etan(4x). Differentiate the given expression with respect to x.…

Q: 2. Determine the second derivative of f(x) = x²e²* at x = -2 with a step-size of h=0.50 using…

A: Given function f(x)=x2e2x. The objective is to determine the second derivative of fx at x=-2 with a…

Q: Find the derivative and simplify exy -x² = 4Y² %3D

A:

Q: Find the derivative of x2cosx+2xsin x O 2xcos x O x² sin x + 2xcos x Ọ xzcosx y=x²sinx

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Q: Compute the derivative of the function y = 6 cos- (7x) at the point x = (Use symbolic notation and…

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Q: Find the derivative of f (x ) =V sech( In (8x + 1)) - sech(In(8x + 1)) tanh( In(8x + 1)) A 2/ sech(…

A:

Q: Approximate the derivative of f(x) = x² + 4x + 5 at x = 3 using the forward, backward, and central…

A: f(x) = x2 + 4x + 5 h = Δx = 2 xi = 3         f(xi) = 26 xi+1 = 5          f(xi+1) = 50 xi-1 = 1…

Q: What is the approximate derivative of f(x) = x2e* , using backward-difference approach at %3D x-2…

A: The main objective is to calculate the value of the derivative of the function f(x)=x2ex at the…

Q: Find The derivaTive of f(X) = -x²+ 3X + 2 Using the de finiTion of the derivative

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Q: 3. FIND THE DERIVATIVE BY THE LIMIT PROCESS OFF (x) = Vx + 2.

A:

Q: Find the derivative of f(x) = 9 sinh-' (x²) – 9 In ( Vx4 + 1). %3D

A:

Q: Find the derivative of the function. InV y = In 6 - X %3D y' = %3D

A: Explanation of the answer is as follows

Q: Find the derivative using the long method 3-t to

A:

Q: Find the derivative of f(x)  =(a + 2x2) (x - x2) in twoways: by using the Product Rule and by…

A: We have given function  fx=a+2x2x-x2 At first we  will use product rule:…

Q: Зx+1 5. f(x) %3D 3x2+2

A: f(x)=3x+13x2+2Differentiate…

Q: ,2, (x²–1)* Dx (1+8x)5

A: To Determine: find the derivative using chain rule  Given: we have y=x2-141+8x5 Explanation: we have…

Q: Find the relative extremum of g(x) = x - 3x +1 by using first derivative test.

A: Let g(x)= x3-3x2+1 To find the relative extremum , here we use first derivative test In this method…

Q: Find the derivative of f ( x ) = 6 sin ^2 ⁡( x ) + 6 cos^2 ⁡( x ) at x = -6.5

A:

Q: Find sixth order derivative of the function f(x) = (x – 5)7.cos(5x) by using %3D Leibnitz theorem.

A: If y=uv where, u and v are functions of x then un and vn denote the nth derivative of u and v with…

Q: Compute the derivative for y= (e^-4x sin^2(x)) / (x^2 + 3x + 1)

A:

Q: Find the derivative of y with respect to x. 6x + 7 -1 6. y3-Cos %3D

A: dydx=?

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

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

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Q: Find 1" and 2nd order partial derivative for the function ax²+by²+2hxy and also verify дхду дудх

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Q: Find the derivative of f(x) = arctan x In(6x² + 6x – 4) 1 1 arctan x 6x2+6x-4

A: Here the given function fx=tan-1x ln6x2+6x-4

Q: r(x)= cos (3x)

A: