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

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

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

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

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(x^{3} \cdot 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)

y^{\frac{1}{2}} \cdot \frac{d y}{d x} + y^{\frac{3}{2}} = 1

\int \frac{1}{3 sin ^{2} ( x ) + 5 cos ^{2} ( x )} d x

\frac{d}{d x} (2 sin (x) + sin (2 x))

\int \frac{15}{15 + e ^{x}} d x

\int_{0}^{100} \frac{1}{x} d x

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