What is the derivative of 8(sin(x))^x ?

The derivative of 8(sin(x))^x is 8sin^x(x)(ln(sin(x))+xcot(x))

What is the first derivative of 8(sin(x))^x ?

The first derivative of 8(sin(x))^x is 8sin^x(x)(ln(sin(x))+xcot(x))

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derivative of

8 (sin (x))^{x}

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

Solution steps

\frac{d}{d x} (8 (sin (x))^{x})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 8 \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))}

= 8 \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)

= 8 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)

= 8 sin^{x} (x) (ln (sin (x)) + x cot (x))

\frac{d}{d x} (\frac{1}{ln ( x )})

n = 1 \sum \infty 3 (\frac{7}{2})^{n - 1}

x \to 0 + lim (tan (3 x))

\frac{d}{d x} (0.5 x^{3})

What is the derivative of 8(sin(x))^x ?
The derivative of 8(sin(x))^x is 8sin^x(x)(ln(sin(x))+xcot(x))
What is the first derivative of 8(sin(x))^x ?
The first derivative of 8(sin(x))^x is 8sin^x(x)(ln(sin(x))+xcot(x))