What is the derivative of log_{10}(x^7+5) ?

The derivative of log_{10}(x^7+5) is (7x^6)/(ln(10)(x^7+5))

What is the first derivative of log_{10}(x^7+5) ?

The first derivative of log_{10}(x^7+5) is (7x^6)/(ln(10)(x^7+5))

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derivative of

lo g_{10} (x^{7} + 5)

\frac{7 x ^{6}}{ln ( 10 ) ( x ^{7} + 5 )}

Solution steps

\frac{d}{d x} (lo g_{10} (x^{7} + 5))

Apply log rule:

lo g_{a} (b) = \frac{ln ( b )}{ln ( a )}

= \frac{d}{d x} (\frac{ln ( x ^{7} + 5 )}{ln ( 10 )})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{ln ( 10 )} \frac{d}{d x} (ln (x^{7} + 5))

Apply the chain rule:

\frac{1}{x ^{7} + 5} \frac{d}{d x} (x^{7} + 5)

= \frac{1}{x ^{7} + 5} \frac{d}{d x} (x^{7} + 5)

\frac{d}{d x} (x^{7} + 5) = 7 x^{6}

= \frac{1}{ln ( 10 )} \cdot \frac{1}{x ^{7} + 5} \cdot 7 x^{6}

Simplify

\frac{1}{ln ( 10 )} \cdot \frac{1}{x ^{7} + 5} \cdot 7 x^{6} : \frac{7 x ^{6}}{ln ( 10 ) ( x ^{7} + 5 )}

= \frac{7 x ^{6}}{ln ( 10 ) ( x ^{7} + 5 )}

\frac{d}{d x} (\frac{1}{3 x ^{\frac{2}{3}}})

\int x (x^{2} - \frac{1}{x}) d x

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

f (x) = \frac{3 x - 7}{5 x - 2}

\frac{d}{d x} (\frac{2}{3} x^{2} - 5 x + \frac{3}{x} + 7)

What is the derivative of log_{10}(x^7+5) ?
The derivative of log_{10}(x^7+5) is (7x^6)/(ln(10)(x^7+5))
What is the first derivative of log_{10}(x^7+5) ?
The first derivative of log_{10}(x^7+5) is (7x^6)/(ln(10)(x^7+5))