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

The derivative of f(x)=x^2sin(sqrt(x)) is 2xsin(sqrt(x))+(x^{3/2}cos(sqrt(x)))/2

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

The first derivative of f(x)=x^2sin(sqrt(x)) is 2xsin(sqrt(x))+(x^{3/2}cos(sqrt(x)))/2

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derivative of

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

2 x sin (x) + \frac{x ^{\frac{3}{2}} cos ( x )}{2}

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

\frac{cos ( x )}{2 x} x^{2} = \frac{x ^{\frac{3}{2}} cos ( x )}{2}

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

\int x + 8 d x

\frac{d}{d x} (x^{2} - 27)

\int ((4 x + 3) (2 x^{2} + 3 x)^{3}) d x

\frac{d ^{2}}{d x ^{2}} ((9 x^{2} + 6)^{7})

(- 2.5) (- 4.1)

What is the derivative of f(x)=x^2sin(sqrt(x)) ?
The derivative of f(x)=x^2sin(sqrt(x)) is 2xsin(sqrt(x))+(x^{3/2}cos(sqrt(x)))/2
What is the first derivative of f(x)=x^2sin(sqrt(x)) ?
The first derivative of f(x)=x^2sin(sqrt(x)) is 2xsin(sqrt(x))+(x^{3/2}cos(sqrt(x)))/2