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Popular >

derivative of f(x)=4^x-x^2+3ln(x)

Solution

derivative of

f (x) = 4^{x} - x^{2} + 3 ln (x)

Solution

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

Solution steps

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

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (4^{x}) - \frac{d}{d x} (x^{2}) + \frac{d}{d x} (3 ln (x))

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

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

\frac{d}{d x} (3 ln (x)) = \frac{3}{x}

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

Popular Examples

derivative of (40t^2)/(t^2+150)derivative of

\frac{40 t ^{2}}{t ^{2} + 150}

limit as x approaches 0+of 3/x-2/(ln(x))

x \to 0 + lim (\frac{3}{x} - \frac{2}{ln ( x )})

integral of (-1)/(x^3)

\int \frac{- 1}{x ^{3}} d x

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

\int_{- 2}^{2} \frac{1}{x ^{2}} d x

integral of 2e^x+2x-1

\int 2 e^{x} + 2 x - 1 d x

Frequently Asked Questions (FAQ)

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