What is the (x^3cos(x))^' ?

The (x^3cos(x))^' is 3x^2cos(x)-x^3sin(x)

What is the first (x^3cos(x))^' ?

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

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(x^{3} cos (x))^{^{'}}

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

Solution steps

(x^{3} cos (x))^{'}

Apply the Product Rule:

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

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

= (x^{3})^{^{'}} cos (x) + (cos (x))^{^{'}} x^{3}

(x^{3})^{'} = 3 x^{2}

(cos (x))^{'} = - sin (x)

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

Simplify

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

\int \frac{1}{16 x ^{4} - 8 x ^{2} + 1} d x

n = 0 \sum \infty \frac{4 n}{8 n + 5}

\int_{1}^{2} \frac{ln ( x )}{x ^{3}} d x

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

y = x^{2} - 5 x, (5, 0)

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