What is the derivative of y=x^2cos(x) ?

The derivative of y=x^2cos(x) is 2xcos(x)-x^2sin(x)

What is the first derivative of y=x^2cos(x) ?

The first derivative of y=x^2cos(x) is 2xcos(x)-x^2sin(x)

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derivative of

y = x^{2} cos (x)

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

Solution steps

\frac{d}{d x} (x^{2} cos (x))

Apply the Product Rule:

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

f = x^{2}, g = cos (x)

= \frac{d}{d x} (x^{2}) cos (x) + \frac{d}{d x} (cos (x)) x^{2}

\frac{d}{d x} (x^{2}) = 2 x

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

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

Simplify

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

\frac{d y}{d x} = 4 x 4 - y^{2}

\int x sin (ln (x)) d x

\int_{4}^{\infty} e^{- \frac{x}{2}} d x

\int \frac{ln ( x ) + 10}{x} d x

5 - x^{2}

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