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

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = sin (x^{3}), g = cos^{3} (x)

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

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

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

= cos (x^{3}) \cdot 3 x^{2} cos^{3} (x) + (- 3 cos^{2} (x) sin (x)) sin (x^{3})

Simplify

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

\int \frac{4}{- 4 x ^{2} - 20 x - 9} d x

f (x) = \frac{1}{x}, (- 1, - 1)

y^{^{'}} - 2 y = x^{2} + 5

\int \frac{1}{x ( x ^{7} + 1 ) ^{2}} d x

y = 2 \cdot x^{5} - 3 \cdot x \cdot e^{- x} - 10

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