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

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

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

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

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derivative of

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

2 sin^{2 x} (x) (ln (sin (x)) + x cot (x))

Solution steps

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

Simplify

((sin (x))^{x})^{2} : sin^{2 x} (x)

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

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

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

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

= 2 sin^{2 x} (x) (ln (sin (x)) + x cot (x))

2 x^{3} - 3

\frac{1}{2 x}

3 ln (e^{x})

y = sin^{3} (1 - 2 x)

(x^{2} + 1)^{\frac{1}{2}} - 1

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