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

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

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

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

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derivative of

(sin (x))^{x}

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

Solution steps

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

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

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

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

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

\int 30 x^{5} d x

x^{3} - 2 x + 2 (4.58)

\frac{\partial}{\partial x} (3 x - 7 y)

y^{^{'}} cos (x) + y sin (x) = 2 cos^{3} (x) sin (x)

h \to 0 lim (\frac{2 ^{- h} - 1}{h})

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