What is the derivative of (2-x^2cos(x)+2xsin(x)) ?

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

What is the first derivative of (2-x^2cos(x)+2xsin(x)) ?

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

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

x^{2} sin (x)

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

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

= x^{2} sin (x)

x \to \infty lim (5)

\frac{d}{d x} (\frac{- 8}{x})

\frac{d ^{2}}{d x ^{2}} (x^{2} + y^{2})

f (x) = x x, (1, 1)

\int e^{4 x} sin (5 x) d x

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