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Popular >

derivative of ln(1+4^x)

Solution

derivative of

ln (1 + 4^{x})

Solution

\frac{ln ( 2 ) \cdot 2 ^{2 x + 1}}{1 + 4 ^{x}}

Solution steps

\frac{d}{d x} (ln (1 + 4^{x}))

Apply the chain rule:

\frac{1}{1 + 4 ^{x}} \frac{d}{d x} (1 + 4^{x})

= \frac{1}{1 + 4 ^{x}} \frac{d}{d x} (1 + 4^{x})

\frac{d}{d x} (1 + 4^{x}) = ln (2) \cdot 2^{2 x + 1}

= \frac{1}{1 + 4 ^{x}} ln (2) \cdot 2^{2 x + 1}

Simplify

\frac{1}{1 + 4 ^{x}} ln (2) \cdot 2^{2 x + 1} : \frac{ln ( 2 ) \cdot 2 ^{2 x + 1}}{1 + 4 ^{x}}

= \frac{ln ( 2 ) \cdot 2 ^{2 x + 1}}{1 + 4 ^{x}}

Popular Examples

(dy)/(dx)=x^7-1/(x^7)

\frac{d y}{d x} = x^{7} - \frac{1}{x ^{7}}

derivative of sqrt(3+4x^2+9x^4)

\frac{d}{d x} (3 + 4 x^{2} + 9 x^{4})

integral from 0 to 1 of 2pix(2e^{-x^2})

\int_{0}^{1} 2 π x (2 e^{- x^{2}}) d x

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\int_{0}^{π} t cos (2 t) d t

integral of ((x-2)(x+3))/(xsqrt(x))

\int \frac{( x - 2 ) ( x + 3 )}{x x} d x

Frequently Asked Questions (FAQ)

What is the derivative of ln(1+4^x) ?
The derivative of ln(1+4^x) is (ln(2)*2^{2x+1})/(1+4^x)
What is the first derivative of ln(1+4^x) ?
The first derivative of ln(1+4^x) is (ln(2)*2^{2x+1})/(1+4^x)