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Question

How do you find the derivative of y=cos(3x) ?


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Solution

Solve for differentiation:

Given: dydx=ddx(cos(3x))
we know that ddx(cos(x))=-sin(x)

applying chain rule df(g(x))dx=dd(g(x))f(g(x))×dg(x)dx

Here, g(x)=3x and f(g(x))=cos(3x)

ddx(cos(3x))=dd(3x)(cos(3x))×ddx(3x)

dydx=(-sin(3x))ddx(3x)

dydx=(-sin(3x))3dydx=-3sin(3x)

Hence, the derivative of y=cos(3x) is dydx=-3sin3x.


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