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

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

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

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

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

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

Solution steps

\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))

\frac{d}{d x} ((sin (4 x))^{6 x})

cos (2 x^{3})

\int_{0}^{2} \frac{3}{x ^{2} + 4} d x

\frac{d}{d x} (arccos (2 x))

\frac{\partial}{\partial x} (12 x y e^{- x^{2} - y^{2}})

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