Use the rules of differentiation that we learned in class to find the first derivative of each of the following functions: 3 a. f(x) = -5e* ++7/x7 2x 4 + 3x5 5x3 b. f(x) = %3D

Q: Use the alternative form of the derivative to find the derivative at x = c, if it exists.   h(x) =…

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Q: Use the alternative form of the derivative to find the derivative at x = c (if it exists). (If the…

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Q: Find the first derivative of y with respect to x (y') of the given function using rules for…

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Q: Compute the derivative of the following function. f(x) = 3x + 5x ex f'(x) = [ O

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Q: (c) F(x) 3 (х + х-1)3

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Q: Find the derivative of the following functions by applying “Delta Method". Show your complete…

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Q: H(x) = 2x3- 3x + 4 Зх + 4 %3D

A: Hx=2x3-3x+4

Q: For the given function f(x), determine the equation of the tangent line at the point P(1,1) f(x) =…

A: Equation of tangent line

Q: Use the alternative form of the derivative to find the derivative at x=c ( if it exists). f(x) =…

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Q: By implicit differentiation, find if y = x2 + 3x + 1 and x = t2 + 2. dt

A: Given,  y=x2+3x+1 and x=t2+2

Q: calculate the derivative with respect to x. xey = 2xy + y3

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Q: Use the alternative form of the derivative to find the derivative at x = c, if it exists. f(x) = ∣x…

A: Concept: Derivative is the amount by which function is changing at one point. Given:

Q: Use the quotient rule to find the derivative of the following. x2 - 9x + 1 y% = x2 +2 dy dx

A: See attached file for a step by step explanation.

Q: Compute the derivative of the following function. f(x) = 3x + 7x eX f'(x) =D

A: f(x)=3x+7xexfI(x)=?

Q: Use three-point midpoint formula to evaluate the first derivative of y = x² + 4x − 5 at x = 0 using…

A: The given problem is to find the first derivative of the given function at x=0 with given h value by…

Q: Y = (cot x)3x² 3r2

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Q: Find the derivative of f(x) = 8e7x +e=x? f'(x) =

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Q: Find the given higher-order derivative. F(3)(x) = Vx², f(4)(x) f(4)(x) =

A: Given that, the higher order derivative f(3)(x) = x23 To find the higher order derivative of f(4)(x)…

Q: Compute the derivative of the following function. 1(x) = 3e 3x f'X)%3D

A: Topic - differentiation

Q: Use the alternative form of the derivative to find the derivative at x = c  (if it exists). f(x) =…

A: Definition used -           Alternative form of derivative -…

Q: Use three-point midpoint formula to evaluate the first derivative of y = x – 4 at x of h = 5. O…

A: Find the first derivative of y=x3-4 at x=0 using the three-point midpoint formula with h=12.

Q: FIND THE DERIVATIVE OF THE GIVEN 4.) f(x) = sec x ニ 5.) y= In「3-2メ |- 3x 6.) y= Inle-*+ xe-*)

A: 4. To find: The derivative of the function. Given: The function is secx. Calculation: Use the chain…

Q: Use the alternate form of the derivative to find the derivative at x=c, if it exists. f(x) = x³ +…

A: Given f(x) = x³ + 2x² + 1, c = -2 Find the derivative at x= c if exist by using the alternate form…

Q: Find the derivative of the function w, below. It may be to your advantage to simplify first. y 6y +…

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Q: Use the rules of differentiation to find the derivative of the function             g(t) = 2/3t2

A: Given,           g( t ) = 23t2

Q: Use the definition of the derivative to show that the derivative of y = f(x)3 2/ is 1 f'(z) = VI %3D

A: GIVEN f(x) = 2√ x CALCULATE f'(x) = 1/ √ x

Q: Use the alternative form of the derivative to find the derivative at x = c, if it exists. f(x) = x3…

A: Given: fx=x3+2x2+1 , c=-2 To determine: Derivative of given function at x=c

Q: 1 f(y) = y² )(y + 5y³) y4,

A: let us simplify function firstf(y)=(1y2-1y4)(y+5y3)=(y2-1y4)(y+5y3)=y3+5y5-y-5y3y4=5y5-y-4y3y4it can…

Q: Find the derivative of the function and then evaluate at the given point. y= 4x2 - 5x; (– 1,9) f'(x)…

A: The given function is y=4x2-5xThe point is (-1, 9)

Q: Use the alternative form of the derivative to find the derivative at x = c (if It exists). f(x) = x2…

A: Given f(x)=x2-2 c=5

Q: Find the derivative of the following function .1 F(x) = ds 5 + 3s4

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Q: Use the Chain Rule combined with other differentiation rules to find the derivative of the following…

A: Given: y=xx+15 To Find: The derivative of the given function

Q: Calculate the derivative of the function y = (6^6 + 3)^x using the fact that b^x = e^(x ln b) and by…

A: Consider the given function:

Q: Find the derivative of the given functions: 2. f(x) = rcos(rx) – 6 sec(x) + 3

A: Given that, f(x)=rcos(rx)-6secx+3When r=4we have,f(x)=4cos(4x)-6secx+3

Q: Use the rules of differentiation to find the derivative of the function.                y = t2 − 3t…

A: Differentiation: y=t2-3t+1Derivative of the function we need to find out.We knowddx(xn)=n.xn-1

Q: Use the table of values to calculate the derivative of the function at the given point. 1 4 6. f(x)…

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Q: 2x f{X) = 1+ X

A: Given: f(x)=2x1+x

Q: Use the rule of differentiation to find the derivative of the given functions 1. y = (4x – 1)5 2.…

A: 1. y=(4x-1)5, Taking derivative with respect to x, ⇒dydx=5(4x-1)4×ddx(4x-1)         =5(4x-1)4×4…

Q: Find the derivative with respect to x: y = x3- 3*

A: The given function is: y=x3.3xWe need to find the derivative of y with respect x.Recall the…

Q: Use the alternative form of the derivative to find the derivative at x = c, if it exists. f(x) = (x…

A: Given function is fx=x-623. To find the derivaitve of the function at x=c. Differentiating with…

Q: Evaluate the derivative of the following function at the given point. x+ 3x - 5y + 101 = 0: (-3.4)…

A: The objective is to evaluate the derivative of the function at the given point.

Q: 10. G(x) 3ex -7 log, x - 2x %3D

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Q: 3 1 27. y= 2x2 +4.x² – 5 +4x² – 5

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Q: Use the rules of differentiation to find the derivative of the function.                        y =…

A: Given:  y=x2-12 cos x…

Q: f(x) = Vx + 9

A: We have to find the derivative of the function: fx=x+9 We know the formula of differentiation,…

Q: Use the definition of the derivative to find df/dx. f(x) = x/(1-3x)

A: Given, function

Q: Use the rules of differentiation to find the derivative of the function. .            f(t) = −3t2 +…

A: Given : ft = -3t2+2t-4

Q: Use the definition of a derivative to the derivative of the following functions. x + 3 h(x) = 2х -1

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Q: Find the derivative if the following and simply to its simplest fo a) y= (4t2 – 3t + 2)-2 (x+3)* b)…

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