Your Porsche's gas mileage (in miles per gallon) is given as a function M(x) of speed x in miles per hour. It is found that 3,600x-2 - 1 (3,600x-1 + x)2 M'(x) Estimate M'(40), M'(60), and M'(100). (Round your answers to seven decimal places.) M'(40) = mpg/mph M'(60) = mpg/mph M'(100) = mpg/mph

Q: h(x)=(x° +1} (2x+5)*

A: Given : hx = x2+132x+52

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A: y=2cos2 t/2

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A:

Q: Find the derivative of the function y = sech(4x − 1)

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Q: find nth derivative of y=x/(x+1)^4

A: To find the nth derivative of the function y=x(x+1)4=x+1-1(x+1)4=1(x+1)3-1(x+1)4

Q: Find the derivative gx) = 4 K) = cost dt

A: Problem is solved using Leibniz rule

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Q: Find the second derivative of function, and then find ƒ″ (1)  and ƒ″ (−3) .

A: Find first the derivative as shown below: f'x=ddx-5-x2        =125-x2ddx5-x2       =-125-x2-2x…

Q: Find the first derivative of the function Y = [(x – 1)(2x + 3)]?.

A: Let us see the expansion of (a + b - c)2 formula.(a + b - c)2 = (a + b - c)(a + b - c)(a + b - c)2 =…

Q: 10. S(2x – 3) dx e 2x2 - ебх

A:

Q: 4 1 Y(s) = 5s2

A:

Q: 2. f(x) = x2– 5x + 6 at x 2 --

A:

Q: Find the derivative of the function. x + 6 X-6 y' = y = In

A: I have appended the formula used in the solution part of the question.

Q: Compute the second derivative with respect to x of 3x3 + 8 y = at x = 1.

A:

Q: 4. Find the second derivative of Y with respect to x for 4x² + 8y² = 36

A:

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A: We can make it easier for you

Q: 1 Find the function whose derivative is (x+1)-

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A:

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A:

Q: 3x g(x)=e* In(4x+1) (с)

A:

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A:

Q: Q:1 Find the second derivative of f(x) = 2x5 - 3VX7 at x = 1 rounded to five decimal places.

A: To find the second derivative of  f(x)=2x⁵-3x7/3 at x=1

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A:

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A:

Q: Find the derivatives from the left and from the right at x = 1 (if they exist). Is the function…

A: Given: f(x)=(1-x2) Find the derivative of given function from the left and from the right at x = 1…

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A: To determine derivative of the function.

Q: FIND THE DERIVATIVE OF THE FUNCTIONy=0.6e to the fifth(x) degree

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A:

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A:

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A: Formula:

Q: I FIND THE INDICATED DERIVATIVE IN ITS SIMPLIFIED FORM: 3. y = V(4x + 3)³

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A:

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Q: Differentiate the functions: 1. y = 3x – Vx 2. y = 2 – 3x – 3. Given the function f(x) = x³ – 5x +…

A:

Q: 1. What is the derivative of f(x) = x2 – 8x + 12 when you illustrate using tangent? 2. What is the…

A: Note: As per our company guidelines we are supposed to answer the first three sub-parts of the…

Q: Find the nth order derivative of the cube root y=3√x.

A: We first find the first three derivatives using the power rule

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A:

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A:

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A: We have to find

Q: Find the 1st derivative of the function: y = 4(Vx + 1)5

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: