If x is measured in meters and f(x) is measured in newtons,what are the units for  ∫0100 f(x) dx ?

Q: Solve the second derivative forf(x,y, 2) = e

A: Given f(x,y,z)=esin(x²+y²)/z To find del²f/delx²

Q: Find the derivative of the following: y = ln( x^5 + 7) ^ 4pi

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Q: Find the derivative of the exponential function. Y = x'e-5x dy dx

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Q: Find the indicated derivative. 32 df If f(x) =F + 12 x, find dx x = 4 df dx x = 4

A: Topic:- Derivatives

Q: Show that the function f(t) = sin(e*) is of exponential order as t → +oo but that its derivative is…

A: To show that the given function ft=sinet2 is of exponential order.

Q: Find the derivative of the function F(s) = In(9 ln(8s)). F'(s)

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Q: Suppose f(x) = e**+5x+7. Find the df derivative dx f'(x) =

A: We have to find

Q: Compute the indicated derivative. d + 7x)(x2. dx x = 2

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Q: Find the indicated derivative or integral a. D, (3** * ) c. D, log,, (x³ +9) –3x а. D, b. |x 2* dx…

A: We know that Dx ax = ax·ln(a) Dx af(x) = af(x)·ln(a)·f'(x)   ∫ax dx = axln(a)+C   Dx loga x =…

Q: Compute the derivative: d 4 dx x2 5 x=1 The derivative is:

A: The solution of the problem is given in the next step.

Q: Find the equation of tangent at x = In 5: ln 2x a) y = ²x + 1 e to :

A: According to our guidelines, In case of multiple questions we are supposed to answer the first…

Q: What is the value of ln[f'(2)] if f(x) = e^x?

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Q: for f(x) = tan-1G) ду? Solve the second derivative

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Q: In the given question/s , find the derivative of the function.   y = ln l sin x l

A: Consider the function: y=lnsinx

Q: 2x+4 f(x) = (3x + 7) e.

A: Given query is to find the derivative of f(x).

Q: 1. Find and simplify the indicated derivative: (a) D: [e¯t sin(2t)]

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Q: Find the indicated derivative. df If f(x) = x3, find dx 8 df dx |x = -11 || X 32 X = 10 X 1 2 11

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Q: for the function f(x) = 2 cos(45x)o , determine: the instantaneous rate of change at x = 12. you…

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Q: Find a formula for the nth derivative y^n of the function y=(x+5)^1/2

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Q: Find an expression for the derivative of h(x)=ln(f(x)). answer in terms of f and f'.

A: The given function is  h(x) = ln(f(x))

Q: 1. D, (x') 2. D, (5x) 3. D. (x-2x)

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Q: Solve for the following implicit derivative: d²y si sen(y) = ycos(2x) dx?

A: We have to find the double derivative of the given function.

Q: Find the indicated derivative. x2 dz for z = x? + dx 1- x - 5x2 2x – x2 — х dz 2x + (1-x – 5x)2 dx…

A: As per our policy, I can not answer multiple questions and a graded one. Since you have asked for…

Q: Find the equation of the line tangent to xe^1−x at x = 1 and x/e * ln x at x=e.

A: To determine the tangent lines to the curve using derivatives

Q: Find the derivative d/dx of the following 1 log sin(x)

A: We can find the derivative as below

Q: What is the value of the derivative of y=sin(x)cos(x) when a = 2? Write the answer in exact form, an…

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Q: h(x) = e(-1/2)x

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Q: Find the given derivative 6 Dx 7x 1 Dx 7x 5 LN +

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Q: _xe. f(x) = (1+e*)

A: Here we have to find the differentiation of given function. The solution is following.

Q: Find the indicated derivative and simplify. 1 dy 7 for y = 49x' (x' + 10) dx

A: Given that, y=49x17(x7+10)

Q: What is the derivative of (9x² + 14)2 (20x2 +11a- 15)3 123 e y = with respect to x? Hint: Take the…

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Q: (b) Use your answer from part (a) to evaluate the derivative. (ӕ — 5)30 In d dx V (2а — 7)34 -

A: first, simplify the function ddxlnx-5302x-734 =ddxlnx-5302x-73412 =ddxlnx-53022x-7342…

Q: Differentiate the following equation.  f(x)= (ln x)3 ex

A: Given:- f(x) = (ln(x))3 ex  To find :- Differentiate the given function f(x)

Q: d -y(x) if e²-y = sin a d.x

A: We will solve the following

Q: What is the derivative of y = log b( cos² (ax)) ? Note that a and b are real numbers.

A: we have to find derivative

Q: Where is the function sin (log (r2 + y²)) continuous?

A: Function = Sinlogx2+ y2

Q: The derivative of y = e sin(x) sin2(x) can be written as y cos(x)g(x), Determine the value of g(x)…

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Q: - In y = e' sin x

A: We have to find dy/dx of the above equation.

Q: Solve by definition of derivative if f(x)=x+Vx AND also Find x? w.r.t x*

A: fx=x+x Now by the definition of derivative, we have…

Q: y = (1+x)² 2 x² 2

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Q: 1) For #31-34, evaluate each derivative. d 3 dx ' sec /a* dx d. | ytan tdt dx

A: As per the company guidelines we can solve first three parts . I hope that the given solution will…

Q: Compute the indicated derivative. d + x)(x5 – x)]. dx x = 1

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Q: 4. D, (x-2)(2x +3) 5. D, (e")

A: We know that, Dx(ex) =ex Dx(xn) =nxn-1

Q: Find the equation of the tangent line to the function f (x) = e*²-1 ln(x + 1) when x= 0.

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Q: Find the second derivative f"(x) for f(x) = e(#+2)*.

A: First calculate the first derivative for f(x) using the chain rule.…

Q: Find the derivative of the exponential function f ( x ) = 5x 2 e 7x

A: Given function: f(x)=5 x2 e7x     Calculate the derivative of f(x): f(x)=5 x2 e7x   Take the…

Q: Find the indicated derivative. dz if z = In (x° + e 5) dx dz dx

A: Given data is: z=lnx8+e5 To find the value of dzdx

Q: Find the derivative of the function f(x) below. f(x)=ln(5−e^(−4x)) f′(x)=

A: Explanation: Given that, f(x)=ln(5-e-4x) Differentiate both sides with respect to x.…

Q: y = (x² + x + 1)²

A: