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Popular >

derivative of 2^{tan(x})

Solution

\frac{d}{d x} (2^{t a n (x)})

Solution

ln (2) \cdot 2^{t a n (x)} sec^{2} (x)

Solution steps

\frac{d}{d x} (2^{t a n (x)})

Apply exponent rule:

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

2^{t a n (x)} = e^{t a n (x) l n (2)}

= \frac{d}{d x} (e^{t a n (x) l n (2)})

Apply the chain rule:

e^{t a n (x) l n (2)} \frac{d}{d x} (tan (x) ln (2))

= e^{t a n (x) l n (2)} \frac{d}{d x} (tan (x) ln (2))

\frac{d}{d x} (tan (x) ln (2)) = ln (2) sec^{2} (x)

= e^{t a n (x) l n (2)} ln (2) sec^{2} (x)

e^{t a n (x) l n (2)} = 2^{t a n (x)}

= ln (2) \cdot 2^{t a n (x)} sec^{2} (x)

Graph

Popular Examples

integral from 1 to 2 of 2(x-1)

\int_{1}^{2} 2 (x - 1) d x

integral of (x^2)/(sqrt(4+x^2))

\int \frac{x ^{2}}{4 + x ^{2}} d x

integral of (x^4+1)/(x^3-x^2+x-1)

\int \frac{x ^{4} + 1}{x ^{3} - x ^{2} + x - 1} d x

integral of-2e^{-x}

\int - 2 e^{- x} d x

derivative of f(x)=e^{3x}sin(3x)derivative of

f (x) = e^{3 x} sin (3 x)

Frequently Asked Questions (FAQ)

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