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Popular >

derivative of 2^{sin(x)}

Solution

derivative of

2^{s i n (x)}

Solution

ln (2) \cdot 2^{s i n (x)} cos (x)

Solution steps

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

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

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

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

= ln (2) \cdot 2^{s i n (x)} cos (x)

Popular Examples

derivative of-(200ln(x/(40))/(x+20))

\frac{d}{d x} (- \frac{200 ln ( \frac{x}{40} )}{x + 20})

derivative of ln((x+1^2))

\frac{d}{d x} (ln ((x + 1)^{2}))

(\partial)/(\partial x)(1/(x-a))

\frac{\partial}{\partial x} (\frac{1}{x - a})

integral of sin(x)sec^2(x)

\int sin (x) sec^{2} (x) d x

(\partial)/(\partial x)(4x^3+4xy^2)

\frac{\partial}{\partial x} (4 x^{3} + 4 x y^{2})

Frequently Asked Questions (FAQ)

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