# Need derivative help?

find the derivative of z(x)=sin(cos(tan(3x)))

I'm just really confused, please try and be a detailed at possible so I can better understand.

### 1 Answer

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- 1 month agoBest Answer
I showed you the derivative. This is just a chain rule problem

f(t) = sin(t)

f'(t) = cos(t) * d/dt

g(t) = cos(t)

g'(t) = -sin(t) * d/dt

h(t) = tan(t)

h'(t) = sec(t)^2 * d/dt

j(t) = 3t

j'(t) = 3 * d/dt

k(t) = f(g(h(j(t))))

k'(t) = f'(g(h(j(t)))) * g'(h(j(t))) * h'(j(t)) * j'(t)

z'(x) = cos(cos(tan(3x))) * (-sin(tan(3x))) * sec(3x)^2 * 3 * 1

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the " d / dt 's " don't belong....df / dx = [ df /dg][dg/dh][dh/dj][dj/dt] by the 'chain rule'....and df/dg = cos g , ...