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

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

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

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

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

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

Solution steps

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

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

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

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

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

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