What is the derivative of 2sin^3(x-3cos^2(x)) ?

The derivative of 2sin^3(x-3cos^2(x)) is 6sin^2(x)cos(x)+3sin(2x)

What is the first derivative of 2sin^3(x-3cos^2(x)) ?

The first derivative of 2sin^3(x-3cos^2(x)) is 6sin^2(x)cos(x)+3sin(2x)

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\frac{d}{d x} (2 sin^{3} (x) - 3 cos^{2} (x))

6 sin^{2} (x) cos (x) + 3 sin (2 x)

Solution steps

\frac{d}{d x} (2 sin^{3} (x) - 3 cos^{2} (x))

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (2 sin^{3} (x)) - \frac{d}{d x} (3 cos^{2} (x))

\frac{d}{d x} (2 sin^{3} (x)) = 6 sin^{2} (x) cos (x)

\frac{d}{d x} (3 cos^{2} (x)) = - 3 sin (2 x)

= 6 sin^{2} (x) cos (x) - (- 3 sin (2 x))

Simplify

= 6 sin^{2} (x) cos (x) + 3 sin (2 x)

\int \frac{5}{32} x^{4} d x

x sin (\frac{1}{x})

\frac{\partial}{\partial y} (y cos (y - 2 x))

\int y e^{2 y} d y

\int \frac{6 x ^{5} + 6}{( x ^{6} + 6 x ) ^{2}} d x

What is the derivative of 2sin^3(x-3cos^2(x)) ?
The derivative of 2sin^3(x-3cos^2(x)) is 6sin^2(x)cos(x)+3sin(2x)
What is the first derivative of 2sin^3(x-3cos^2(x)) ?
The first derivative of 2sin^3(x-3cos^2(x)) is 6sin^2(x)cos(x)+3sin(2x)