What is the derivative of 7^xln(x) ?

The derivative of 7^xln(x) is ln(7)*7^xln(x)+(7^x)/x

What is the first derivative of 7^xln(x) ?

The first derivative of 7^xln(x) is ln(7)*7^xln(x)+(7^x)/x

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\frac{d}{d x} (7^{x} ln (x))

ln (7) \cdot 7^{x} ln (x) + \frac{7 ^{x}}{x}

Solution steps

\frac{d}{d x} (7^{x} ln (x))

Apply the Product Rule:

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

f = 7^{x}, g = ln (x)

= \frac{d}{d x} (7^{x}) ln (x) + \frac{d}{d x} (ln (x)) 7^{x}

\frac{d}{d x} (7^{x}) = 7^{x} ln (7)

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

= 7^{x} ln (7) ln (x) + \frac{1}{x} \cdot 7^{x}

\frac{1}{x} \cdot 7^{x} = \frac{7 ^{x}}{x}

= ln (7) \cdot 7^{x} ln (x) + \frac{7 ^{x}}{x}

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What is the derivative of 7^xln(x) ?
The derivative of 7^xln(x) is ln(7)*7^xln(x)+(7^x)/x
What is the first derivative of 7^xln(x) ?
The first derivative of 7^xln(x) is ln(7)*7^xln(x)+(7^x)/x