| If (x) – g(x)[dx represents. Explain what

Q: Can you help me with this problem step by step?

A: The logarithmic expression

Q: Write down the limit definition of the derivative f'(x) and USE IT to find d/dx(1/x)

A: Write down the limit definition of the derivative f'(x) and USE IT to find d/dx(1/x)

Q: f(x+h) – f(x), Use the definition of the derivative (that is, f'(x) = lim h0 3 = 3r2. dr to show…

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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: 3 Find the derivative of f(x) = x°e*.

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

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Q: Use derivatives to find two positive numbers a and b such that: a^2 +b^2 = 1 and 2a+3b is as…

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Q: The derivative of y= xh* is O 1) (In x)(xh*-) O 2) 2 an x)(xh*) O 3) (In x)* O 4) xhx

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

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Q: FIND ANTI DERIVATIVE a) S 2. +9 dx x マ d x 1-4x6

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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: Give two applications of the derivative f(x + h) - f(x) f'(x) = lim h

A: The given function f'x=limh→0f(x+h)-f(x)h is the derivative by first principle.

Q: Find the second derivative. 1 h(x) = x2 %3D | h"(x) = %3D

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Q: Compute the derivatives: d/dx [ f (x)g (x)]

A: Derivative of function of type uv is given by, duvdx=v.dudx+u.dvdx

Q: x²+x' Evaluate the derivative at x = 1 for y = In () %3D

A: Some common derivatives are, ddx(ax)=ax.loga+C ddx(logf(x)=1f(x).f'(x)+C Quotient rule of…

Q: V². Find the derivative of f(x) = In x² +1 %3D x(2r - 1)2

A: Derivative: f(x)=lnx2+1x(2x3-1)2ln(mn)=ln m-ln nln(x2+1)=12ln(x2+1)

Q: Evaluate the function: dx ¤(1+x?)

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

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Q: Vhat is the second derivative of f(x) = x'e? II

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Q: Q2/ Discuss the relationship between the derivative and (Lim) with drawing if it is dx required ?

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Q: Find the general anti-derivatives. Evaluate ∫ x/(x-1)(x+2) dx

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Q: - [5√3x d dx

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Q: Find the derivative. f(x) = e° . 7* f' (x) =

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Q: Let f(x) = derivative f'(x) equals o. e. Find the value of x for which the second

A: Given that: f(x)=32x2-ex

Q: %3D Apply the Chain Rule to find the tangent line to f(x) = 4v2x- 6e2-*at x = 2

A: We want to find the tangent of the given function at x=2 We know that slope of the tangent at a…

Q: Find the anti-derivative of g (x)=−8ex+4 − 5/ x+7. (Do not include the constant C in your answer.)

A: We have to find the antiderivative of g(x) .g(x) is given by:

Q: Find the derivative: n[(x³ + 2) (x² + 3)]. Evaluate S dx. Зx8 — 2 2x*- x2 Evaluate dx.

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Q: Suppose f(-3) = 3, f'(-3) = 5, = -8, and %3D g(-3) = 1, gʻ (-3) = H(x) = f(x)e®(x). Find the…

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Q: d By using the definition of the derivative, find the for: dx f(x) = Vx

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Q: For the function f(x) = 3x ln x, find f'(x) =

A: Given functionfx=3x4 .ln x

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

A: Given: fx=ex+24 for finding second derivative of given function we first take log and find first…

Q: Find the derivative of g(x) using first principles. Show your steps. f (x) = %3D 1+3

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Q: Find the derivative. x(x dx d [5x (x* + 1)°]-I dx

A: Given : d/dx[5x(x^4+1)^6]

Q: dy Find dx if y = v5 – x2 ,by using definition .)باستخدام صيغة تعریف المشتقة) formula of derivative

A: Given y=5-x2We know that f'(x)=limh→0f(x+h)-f(x)h...(1)f(x+h)=5-x2-2hx-h2f(x)=5-x2Put all these…

Q: Find f(2x)dx if f(x)dx = 1. Enter the exact answer. f(2x)dx

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Q: Find the derivative. F'(x) if F(x) = (e×" + 1) °

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Q: Find the derivative. f (x) = e* COS X %3D

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Q: Find all the antiderivatives of the following function. Check your work by taking derivatives. g(x)…

A: Given function is gx=11x10. Antiderivative is opposite of derivative. Antiderivative means…

Q: Differentiate the function below y = ln ( ( etan x √(x2 +1) )  /  (x-3)5)

A: We first simplify the given function.  y=lnetanxx2+1(x-3)5y=ln(etanx)+lnx2+1-ln(x-3)5  [addition and…

Q: (a) Find the derivative of y = f(x) =2x+1 using this definition f (x+h)-f(x) f'(x)= lim h (b) If x…

A: Differentiate above function with respect to x

Q: What is the first derivative with respect to x of the function g(x) = 3/9 9. O 1/2

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Q: Find derivative of the following function d -6tanx dx

A: Given query is to find the derivative of the expression.

Q: dy Find dx if y = V5- x2 , by using definition .)باستخدام صيغة تعريف المشتقة( formula of derivative

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Q: Compute the derivative function f' (x) algebraically. f (x) = -5x3 +7 O f' (x) = -15x O f' (x) =…

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

A: Given, function

Q: ind the derivative of h(x) = %3D 4x2+2

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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 function f(x) = 3x? – - 12x – 28 by definition of derivatives f(x + h) –…

A: A function is a relation which maps each value in its domain to exactly one value in its range. The…

Q: Find the derivatives of following functions e2x f(x) 1- ex

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…