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Popular >

derivative of 4^x-e^x+x^3

Solution

\frac{d}{d x} (4^{x} - e^{x} + x^{3})

Solution

ln (2) \cdot 2^{2 x + 1} - e^{x} + 3 x^{2}

Solution steps

\frac{d}{d x} (4^{x} - e^{x} + x^{3})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (4^{x}) - \frac{d}{d x} (e^{x}) + \frac{d}{d x} (x^{3})

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

\frac{d}{d x} (e^{x}) = e^{x}

\frac{d}{d x} (x^{3}) = 3 x^{2}

= ln (2) \cdot 2^{2 x + 1} - e^{x} + 3 x^{2}

Popular Examples

x y + 2 ln (y) y^{^{'}} = 0

integral of (tan^2(3/x))/(x^2)

\int \frac{tan ^{2} ( \frac{3}{x} )}{x ^{2}} d x

e^x*y(dy)/(dx)=e^{-y}+e^{-2x-y}

e^{x} \cdot y \frac{d y}{d x} = e^{- y} + e^{- 2 x - y}

sum from n=9 to infinity of (8/9)^{-n}

n = 9 \sum \infty (\frac{8}{9})^{- n}

integral of 4/(x^3-4x^2+8x)

\int \frac{4}{x ^{3} - 4 x ^{2} + 8 x} d x

Frequently Asked Questions (FAQ)

What is the derivative of 4^x-e^x+x^3 ?
The derivative of 4^x-e^x+x^3 is ln(2)*2^{2x+1}-e^x+3x^2
What is the first derivative of 4^x-e^x+x^3 ?
The first derivative of 4^x-e^x+x^3 is ln(2)*2^{2x+1}-e^x+3x^2