3. Use the Leibnitz formula for differentiation to find(i)dxfor the function y= sin' xIn(ii)for the function y=xe", hence evaluate y'(2).-14. If x 20-sin 20 and y 1- cos 20, show that cote and thatdxdx 4 sine5. If f(x)=|, find the first derivative f'"(x) using first principles.d'y+ tan ydx6. Given that y= tan"(sinh x), show that= 0.dx

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Answered: 3. Use the Leibnitz formula for…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Similar questions

1. Find the second derivative of the following functions with respect to x. y = 3x2 + 5x - 1 2. Find dy/dx by Implicit Differentiation x3 +y3 = 36
1.find the derivative of In[In(Inx)] 2. find the derivative of e(2x+Inx)
Show that x + yx−1 = 1 and y = x − x2 define the same curve [except that (0, 0) is not a solution of the first equation] and that implicit differentiation yields y , = yx−1 − x and y , = 1 − 2x. Explain why these formulas produce the same values for the derivative.
1)Find the anti derivative for sin(x^2) 2x
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find the derivative of y with respect to x, t, or θ, as appropriate. y = (cos θ) ln (2θ + 2)
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3. Use the Leibnitz formula for differentiation to find (i) for the function y=sin" xin) (ii) for the function y x'e", hence evaluate y'(2). dx