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Use the chain rule to differentiate f(t)=e^(4t sin(2t))

Question

Use the chain rule to differentiate f(t)=e^(4t sin(2t))

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Step 1

Let us take u=4tsin(2t) and f(t)=y, then we have y=e^u

(t)= y
u(t)4 sin (2r
,4/sin(2t
ye"
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(t)= y u(t)4 sin (2r ,4/sin(2t ye"

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Step 2

By chain rule of differentiation , we have

f'(t) d du
dt du dt
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f'(t) d du dt du dt

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Step 3

Now , we find dy/du and du/dt  by using the result that derivative of e^u with respect to u is e^u  and b...

dy
y e
du
u() 4tsin (2
du
d
- 4t sin (2r)sin (2t)(4f)
d
dt
dt
du
- 4 [2cos (2)]+ 4sin (2)
dt
8cos(2)4sin (2t)
dt
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dy y e du u() 4tsin (2 du d - 4t sin (2r)sin (2t)(4f) d dt dt du - 4 [2cos (2)]+ 4sin (2) dt 8cos(2)4sin (2t) dt

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Tagged in

Math

Calculus

Derivative

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