What is the derivative of 8^xln(x) ?

The derivative of 8^xln(x) is 3ln(2)*8^xln(x)+(8^x)/x

What is the first derivative of 8^xln(x) ?

The first derivative of 8^xln(x) is 3ln(2)*8^xln(x)+(8^x)/x

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\frac{d}{d x} (8^{x} ln (x))

3 ln (2) \cdot 8^{x} ln (x) + \frac{8 ^{x}}{x}

Solution steps

\frac{d}{d x} (8^{x} ln (x))

Apply the Product Rule:

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

f = 8^{x}, g = ln (x)

= \frac{d}{d x} (8^{x}) ln (x) + \frac{d}{d x} (ln (x)) 8^{x}

\frac{d}{d x} (8^{x}) = 3 ln (2) \cdot 8^{x}

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

= 3 ln (2) \cdot 8^{x} ln (x) + \frac{1}{x} \cdot 8^{x}

\frac{1}{x} \cdot 8^{x} = \frac{8 ^{x}}{x}

= 3 ln (2) \cdot 8^{x} ln (x) + \frac{8 ^{x}}{x}

\frac{\partial}{\partial x} (e^{6 x + 7 y})

\frac{d}{d x} (\frac{2}{1 - 6 x})

\int \frac{1}{9}

\int_{0}^{1} \frac{y}{e ^{4 y}} d y

\frac{d}{d x} (x x + 6)

What is the derivative of 8^xln(x) ?
The derivative of 8^xln(x) is 3ln(2)*8^xln(x)+(8^x)/x
What is the first derivative of 8^xln(x) ?
The first derivative of 8^xln(x) is 3ln(2)*8^xln(x)+(8^x)/x