sin (7x The function y 1) is a composition, and so we must use the Chain Rule, given below, to find the = derivative [f(g(x))] f (g(x))g'(x) dx For the given function sin-2(7x + 1), the "inside" function is 7x 1 and the "outside" function is f(x) = X

Q: Find the derivative of (b) f(x) = 2 tan-1(x) – 7x

A: Givenf(x)= 2 tan-1(x)-7x

Q: (a) Find the derivative. y = ln(4x − 2) − 3 ln(x) dy dx =     (b) Find the derivative. y = ln…

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Q: 1+cscx 7. h(x)=- 1-cscx

A: Given the functionh(x)=1+cscx1−cscx

Q: Find an equation of the tangent line to the graph of the given function at the specified point. f(x)…

A: Consider the given function. fx=5excos x

Q: 6 with respect to x. Find the derivative of y = cos 6. with respect to x is The derivative of y =…

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Q: (x2-1) (x²+1-x) Q4 / Find the equation of tangent line at x = 1, where f(x) x*-x3

A: A tangent line to curve is a line that just touches the curve only one point.

Q: 6. In(x³y²) = x² +y³

A: Let's find second derivative of given function.

Q: Find the derivative of the function. y = sin−1(3x + 1)

A: Given data:     The given function is: y=sin-1(3x+1).   The given function can be expressed as,…

Q: Q3: i) Find the derivative of the function of y = (x² + 1)sin 3x %3D (ii) Find the absolute maximum…

A: Given:  i) y = x2 + 1sin3x ii) f(x) = x2-13, -3≤x≤3

Q: finding the local mins and maximums and the intervals of increase and decrease and making a sign…

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Q: + 4x" + 4х 3D0.

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Q: (b) Using implicit differentiation Find the derivative of 1. y³ + 3x²y = 13 with respect to x and…

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Q: e the chain rule to find and simplify the derivative of the function g(x) = cos(sin1(3x)).

A: Solution:- Differentiate with respect to x with the help of chain rule.

Q: Find the derivative of the function. g(x) = ln(8x + 3) g(x)=

A: We have to find the derivative of the function.g(x) = ln(8x + 3) Here we will use the formula of…

Q: What is the derivative of f(x) · g (x) in terms of f g? -1 Compute the derivative of -sin(x) · 2x…

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Q: y-e" sec! x-3x° 2 csC X Sin x-2X

A: on doing the differentiation of this we get the

Q: The derivative of sin 2x Graph the function y = 2cos 2x for -2 < x< 3.5. Then, on the same screen,…

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Q: Use the General Power Rule, Exponential Rule, or the Chain Rule to compute the derivative. y = cos…

A: topic- derivative of a function

Q: 4. Find the derivative. x? + 6x – 5 (a) 5х -1 (b) ƒ(x) = (3xr² – 5x - 7)' Us e chain rule (c) y =(x-…

A: Topic:- derivatives

Q: en f(x) = (4x + 1)² ' g the chain rule? what is the first step to find f'(x) Find the derivative of…

A: We have to find out derivative using chain rule

Q: Question1. Find the derivative w.r.t x. i. f(x) = Cos (3Vx) f(x) = x - x. Also draw the graph of…

A: given,        1.  fx=cos23x2.  fx=x3-x3.  fx=logxx2+1

Q: Find the derivative of the function. h(x) = 15x14 + 5x? – 2xª + 18x – 6 Step 1 We want to find the…

A: Solution: The objective is to find the derivative of the given function

Q: Use the Chain Rule to find the derivative. y = cos (e40) (Express numbers in exact form. Use…

A: Given.

Q: Find the derivative of f (x) = 5ª ln (x). Enclose arguments of functions, numerators, and…

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Q: II. Find the first derivative of the given function. tan 2x 6. у %3 1-cot 2x

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Q: |(x+ 1) |(x – 1) Find the derivative of k(x) = ln A. k'(x) = x2-1 -1 В. К(х) — (x²+1)

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Q: 3. Find the derivative of y = sin² 3x two different ways, a. Use the product rule. b. Use a power…

A: Here is the solution:

Q: find the derivative of f(x)=x^6e^xcos(x) use symbolic notation and fractions where needed

A:

Q: Given the function f(x) = 3cos(x/2), find the relative extrema on the interval (pi, 7pi) using the…

A: Given that: f(x)=3.cosx2       in (π, 7π)

Q: Find the second derivatives of f(x) = 2x2+3x  3x+5

A: Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: Question1. Find the derivative w.r.t x. f(x) = Cos²(3Vx) f (x) = x3 – x. Also draw the graph of f…

A: Solution:To find the derivative with respect to xFormula:dydx=dydududxddx(cos x)=-sin…

Q: C. Find the derivative of each function. x' - 2x 3. h(x) = 4. F(x)=sin x- cos x- tan x tan x D.…

A: Follow next step

Q: f'(x)= limh->0 (cos (h)-1)/h  this represents the derivative of a function f(x) at a number x=a,…

A: solution is given below

Q: sin x 1) lim- 2) If f (x)=x +1 then the equation of tangent at x-2 is y-4x-3. d 3) dx -2 2

A: find limit using L hospital Rule    Since you have posted a question with multiple sub-parts, we…

Q: a) Using the definition of derivative, calculate the derivative of the function of f(x) = /3x +1 (b)…

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Q: a- y = (cosx) (use logarithm differential) b-y =x.e-.cos5x

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Q: sin(2 x) + 2 Find the function whose derivative is e 2cos x

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Q: (x+ Ax)-S(x) Use the definition of the derivative f'(x) = lim Ax0 to find the equation of the line…

A: Use definition of derivative

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

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Q: хр 8- X 8 + X Find the derivative of y with respect to x. dy In 7 y 3 log 7 |3|

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Q: 2. The function can be differentiated using the Quotient Rule, and the functions x - sec x and xe*…

A: Yes the given statements are correct.Let,f(x) = xx+1f(x) = x+1-1x+1f(x) = x+1-1x+1f(x) =…

Q: Find the second derivative. h(x) = x2 −  1 x2  h''(x) =

A: Given h(x) = (x^2-1)/x^2 Differentiating on both sides with respect to x h'(x) = d/dx(1-x^(-2)) =…

Q: x d) f(x) = x² sin - R e) f(x) = x+₂ x-2

A:

Q: Vx-1 1) Evaluate lim x→1 Vx-1 1-x 2) Find the derivative of y = arctan 1+x

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Q: b. TRUE or FALSE. It is appropriate to use the chain rule to find the derivative of the function f…

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Q: 1-X Find the derivative of y = arctan 1+x

A: Given that: y=arctan1-x1+x

Q: 4x Q No.2. a) Evaluate the derivative of the function: F(x) = Seova (In t) dt. b) Find the…

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Q: (a) Find the second derivative of the function y = 2x² sin(x). (b) Find the derivative of the…

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Q: 22 sin 2 x + 0 x = 0 Let f(x) = (a) Use the chain rule and the product rule to show that f is…

A: The differentiability of a function implies that the derivative at that point is defined. Otherwise,…