What is the derivative of f(x)=log_{10}(x^8+9) ?

The derivative of f(x)=log_{10}(x^8+9) is (8x^7)/(ln(10)(x^8+9))

What is the first derivative of f(x)=log_{10}(x^8+9) ?

The first derivative of f(x)=log_{10}(x^8+9) is (8x^7)/(ln(10)(x^8+9))

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derivative of

f (x) = lo g_{10} (x^{8} + 9)

\frac{8 x ^{7}}{ln ( 10 ) ( x ^{8} + 9 )}

Solution steps

\frac{d}{d x} (lo g_{10} (x^{8} + 9))

Apply log rule:

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

= \frac{d}{d x} (\frac{ln ( x ^{8} + 9 )}{ln ( 10 )})

Take the constant out:

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

= \frac{1}{ln ( 10 )} \frac{d}{d x} (ln (x^{8} + 9))

Apply the chain rule:

\frac{1}{x ^{8} + 9} \frac{d}{d x} (x^{8} + 9)

= \frac{1}{x ^{8} + 9} \frac{d}{d x} (x^{8} + 9)

\frac{d}{d x} (x^{8} + 9) = 8 x^{7}

= \frac{1}{ln ( 10 )} \cdot \frac{1}{x ^{8} + 9} \cdot 8 x^{7}

Simplify

\frac{1}{ln ( 10 )} \cdot \frac{1}{x ^{8} + 9} \cdot 8 x^{7} : \frac{8 x ^{7}}{ln ( 10 ) ( x ^{8} + 9 )}

= \frac{8 x ^{7}}{ln ( 10 ) ( x ^{8} + 9 )}

e^{s i n (x)}

\frac{d}{d y} (\frac{y ^{3} - 8}{y ^{3} + 8})

\int e^{x} (x^{2} + 2 x) d x

\frac{\partial}{\partial x} x c^{2} \frac{1}{1 - \frac{v ^{2}}{c ^{2}}} - 1

\int_{0}^{1} \frac{t}{( 2 - t ) ^{2}} d t

What is the derivative of f(x)=log_{10}(x^8+9) ?
The derivative of f(x)=log_{10}(x^8+9) is (8x^7)/(ln(10)(x^8+9))
What is the first derivative of f(x)=log_{10}(x^8+9) ?
The first derivative of f(x)=log_{10}(x^8+9) is (8x^7)/(ln(10)(x^8+9))