What is the derivative of x^{2sin(x}) ?

The derivative of x^{2sin(x}) is 2x^{2sin(x)}(cos(x)ln(x)+(sin(x))/x)

What is the first derivative of x^{2sin(x}) ?

The first derivative of x^{2sin(x}) is 2x^{2sin(x)}(cos(x)ln(x)+(sin(x))/x)

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\frac{d}{d x} (x^{2 s i n (x)})

2 x^{2 s i n (x)} (cos (x) ln (x) + \frac{sin ( x )}{x})

Solution steps

\frac{d}{d x} (x^{2 s i n (x)})

Apply exponent rule:

a^{b} = e^{b l n (a)}

x^{2 s i n (x)} = e^{2 s i n (x) l n (x)}

= \frac{d}{d x} (e^{2 s i n (x) l n (x)})

Apply the chain rule:

e^{2 s i n (x) l n (x)} \frac{d}{d x} (2 sin (x) ln (x))

= e^{2 s i n (x) l n (x)} \frac{d}{d x} (2 sin (x) ln (x))

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

= e^{2 s i n (x) l n (x)} \cdot 2 (cos (x) ln (x) + \frac{sin ( x )}{x})

e^{2 s i n (x) l n (x)} = x^{2 s i n (x)}

= 2 x^{2 s i n (x)} (cos (x) ln (x) + \frac{sin ( x )}{x})

f (x) = 2 π x^{2}

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

\frac{\partial}{\partial x} ((ln (x^{2} + y^{2}))^{\frac{1}{2}})

\int (x - 2 y) d y

\frac{18}{x}

What is the derivative of x^{2sin(x}) ?
The derivative of x^{2sin(x}) is 2x^{2sin(x)}(cos(x)ln(x)+(sin(x))/x)
What is the first derivative of x^{2sin(x}) ?
The first derivative of x^{2sin(x}) is 2x^{2sin(x)}(cos(x)ln(x)+(sin(x))/x)