What is the derivative of f(x)=x^2sin(x)+2xcos(x) ?

The derivative of f(x)=x^2sin(x)+2xcos(x) is x^2cos(x)+2cos(x)

What is the first derivative of f(x)=x^2sin(x)+2xcos(x) ?

The first derivative of f(x)=x^2sin(x)+2xcos(x) is x^2cos(x)+2cos(x)

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derivative of

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

x^{2} cos (x) + 2 cos (x)

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

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

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

\frac{d y}{d x} = x y + 2 y

y^{^{''}} - 10 y^{^{'}} + 25 y = \frac{4.5 e ^{5 t}}{tt + 1}

\frac{d y}{d x} = 6 x^{5} cos^{2} (y)

\int \frac{11 x}{x ^{4} + 1} d x

\int cot^{3} (x) (sec^{2} (x) - 1) d x

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