x? – 7x + 12 Consider the function f(æ) x – 5 a. Find the first derivative. f'(x) : b. List any critical values. c. Identify intervals of increase.

Q: Q4: a) Use the four steps rule, for find the derivative of function: 1 f (x) = x + 5 b) Find : lim…

A: Solution:

Q: Find the derivative of the function. h(s) = -27s2 + 9

A: topic  -  derivation

Q: Q1) Find the Derivative to the function and find local minimum and local maximum points y = 3x? - 3

A: y=3x2-3 We need to find the derivative of the function and to find the local minimum and local…

Q: II. Obtain the required order of derivative. 1. y? = 4x, find y" 2. x3 - y3 = c³, find y"

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Q: Find the derivative of the function. (x) = e+2 + 3 f'(x) : II

A:

Q: Find all possible functions with the given derivative. y = 5x -7x

A: y'=5x2-7x

Q: Consider the function f(x) = 2x – 3x? – 36x + 54. a. Find the first derivative. f'(x) b. List any…

A:

Q: Calculate the derivative. y = x4 - 4 x² 5 (Give an exact answer. Use symbolic notation and fractions…

A:

Q: Q2. Use the definition of the derivative to find ý of the function y = sin(x). %3D

A: Here given function is  y = sin(x)

Q: Let y=x+∣∣x2−8∣∣. Find the derivative of the function at x=3.

A: Given that y=x+x2-8.

Q: 2. y = 1 (tanh~' 2x)3

A:

Q: Q /Choose the appropriate derivative for this function y = (x + 1)²¯*

A: Given equation:y = (x+1)2-x required:1) dydxSol:y = (x+1)2-x →taking logarithms on both sides we…

Q: 3e* Find the first derivative: f(x) = x (x+1)

A:

Q: x + Va x2 1. Find the derivative of the function f(x) = in two different ways. Once with the…

A: 1 Given function,                  f(x) = x+xx2Differentiate f(x) with respect to x, using quotient…

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

A:

Q: Sx2 - 1 x > 1 (1- x, x < 1' 3. Show that the function f (x) = has no derivative at x = 1.

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Q: Use the Chain Rule to find the derivative of the function. y = (x + Sx?)-1

A: Derivative of function

Q: Find the derivative of f(x) = e2" (3a? - x)

A:

Q: Q2: A) Find an equation of the line tangent to the function of x2 + (y-x) = 9 at x = 1. dy x-x B)…

A: Equation of tangent line is - y- y1 = m(x-x1)

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

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

A:

Q: Q3/ B) Find the derivative of the following functions. 1. xy=(x-y)'+1 2. y=e*secx

A: For both questions we have to apply chain rule and product rule.

Q: Q15: Find the derivative: f(x) = (In x)?

A:

Q: Find the derivative f'(-1) for f(t) = 5t3 + 2t? – 1

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Q: 5e* Find the derivative of f (x) Зех+1

A:

Q: Consider the function f(x) = 2x – 3x? – 12x + 18. - a. Find the first derivative. f'(x) = b. List…

A:

Q: Find the derivative of f(x)=axe^(-bx+10) Assume that a and b are constants. f′(x)=

A: If fx and gx are two differentiable function then according to product rule of the differentiation,…

Q: Find the derivative of the function y = 1ln(cos 2x)+4tan? (3x) Write the value of y (0) in the box…

A:

Q: Find the derivative of the function. f(x) : et? + 9

A: This question is about finding derivative of function.

Q: Given the function y = f(x) = /x² + 1 a. Use the first derivative to find the intervals

A: The function is given y=fx=x2+1. a To find increasing or decreasing function. y=x2+1 Take the first…

Q: C) Find the derivative of y= (1+ x²)*

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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: t(x)=23x3−10x2+42x+9 Given the function above, use the First Derivative Test to find the local…

A:

Q: Q2:A/ Consider the function f(x) =; a-what are the first and second derivatives? b-what are the…

A: As per our guidelines, we are supposed to solve only first three subparts. Kindly repost other…

Q: 5x Use the derivative to find where the function is increasing y = X+1

A:

Q: A) find the 1000th derivative of the function: y = xe¬x.

A: Find derivative

Q: f(x) = 4e−2xsin(x2) 1. What is the first derivative of the equation? 2. Find f′(−1) manually.

A:

Q: 4x+3 J When solving for the second order derivative of f, it yields to f"(x) = X(Ax+B) Cx³ Suppose…

A: The given function is, fx=4x+3x Differentiating with respect to x,…

Q: Q1) Find the derivative a) f(x) = arctan (e-2x) b) f(x) = [arcsin (2²)]³ C) f(x) = tan (lnx) + 52²

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Q: Find the derivative of the function. h(s) = −2√(5s2 + 3)

A: the given function is: hs=-25s2+3 we have to find the derivative of the given function.

Q: se the definition of the derivative to find the derivative of: f(t) = -4 – 2t. (t) =

A: Topic:- derivatives

Q: Q2: Consider the implicit equation: y² – y – x² = 0 Find the implicit derivative dy/dx, and…

A:

Q: f(x) = √√/5x+8 What is the derivative of f(x)?

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Q: se the first derivative and the second derivative test to determine where each function is…

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Q: Find f"(x). 5, f(x) = / (x² + 7) ª Tip: This question askes for second derivative. Mu

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Q: p>Find the second derivative of f (x) = x*e".

A:

Q: C45 O Use the first derivative test to find the local extrema of f(x) where f(x) = 4x3 - 36x.

A: (A)- local maximum at - root(3) and minimum at root(3)

Q: (a) Find the derivative of the function f(x) = ex-1

A: Note: As per company policy we are supposed to solve only one question. So, kindly repost other…

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: