Find the following for the given equation. r(t) = (e-t, 5t², 7 tan(t)) (a) r(t) (b) r"(t) = (c) Find r'(t) r"(t).

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A: Given y = xtan-1(7x) -114ln(1+49x2)dydx = d xtan-1(7x) -114ln(1+49x2)dxdydx =…

Q: 1. Find the derivative of y(t) = t sin().

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Q: 13x Find the derivative of the function y = 2 tan¬1 (5x ). (Use symbolic notation and fractions…

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Q: If f(x) = 10e" + x°, find f'(x). > Next Question

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Q: If y = 2 + cos (x), find the equation of the tangent line to the curve at x = 37. Tangent line:

A: Topic - Equation of tangent line to curve We are given an equation of the curve y=2+cos(x)

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A: Solve by derivative of given function

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Q: Find f'(t) and simplify your answer. cost f(t) = 1 - 2 sint

A: Given function is a quotient function and we proceed with finding the derivative of f/g…

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Q: y = In [7– 4x² +8x']

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Q: d²y Find the second derivative, dx2 a. x = t² + 1 and y = t³ t2 b. x = 2 · + 2 and y = sin(t + 1)

A: This question can be solved using the concept of second order derivative.

Q: d (1.5ƒ(x))|a=2 dx 10- -х — 2. The line tangent to the graph of f at x = 5 is y = d (4f(x)) x=5-…

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Q: Find the equation of y, given the derivative and the indicated point on the curve. y = dy = 2(x - 1)…

A: y= x^2 - 2x + 3

Q: Find the derivative of: - R(t) = (sin² (3t+1), ln(t² − 1), ²) +1

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Q: (15.) For functions f and g, f(g(x))= x. If f(12) 3 and f'(12)= find the equation of the tangent…

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