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Popular >

derivative of 4^xln(x)

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = 4^{x}, g = ln (x)

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

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

\frac{d}{d x} (ln (x)) = \frac{1}{x}

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

\frac{1}{x} \cdot 4^{x} = \frac{4 ^{x}}{x}

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

Graph

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Frequently Asked Questions (FAQ)

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