   Chapter 2.5, Problem 38E

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# Find the derivative of the function. y = sin ( t + cos t )

To determine

To find:

The derivative of a function

Explanation

Rules:

a) Chain rule: If Fx=fogx=fgx then F'x=f'gx*g'x

b) Power function rule : dxndx=nxn-1

c) Sum rule: d(fx+g(x))dx=d(f(x))dx+d(g(x))dx

d) Rule of derivative of trigonometric function :

ddxsinx=cosx

Given:

y=ft=sin(t+cost)

Calculation:

ft=sin(t+cost)

Differentiate given function w.r.to t

f't=ddtsin(t+cost)

By using chainrule and rule of derivative of trigonometric function,

f't=cost+cost

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