What is the derivative of log_{10}(x^6+3) ?

The derivative of log_{10}(x^6+3) is (6x^5)/(ln(10)(x^6+3))

What is the first derivative of log_{10}(x^6+3) ?

The first derivative of log_{10}(x^6+3) is (6x^5)/(ln(10)(x^6+3))

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\frac{d}{d x} (lo g_{10} (x^{6} + 3))

\frac{6 x ^{5}}{ln ( 10 ) ( x ^{6} + 3 )}

Solution steps

\frac{d}{d x} (lo g_{10} (x^{6} + 3))

Apply log rule:

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

= \frac{d}{d x} (\frac{ln ( x ^{6} + 3 )}{ln ( 10 )})

Take the constant out:

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

= \frac{1}{ln ( 10 )} \frac{d}{d x} (ln (x^{6} + 3))

Apply the chain rule:

\frac{1}{x ^{6} + 3} \frac{d}{d x} (x^{6} + 3)

= \frac{1}{x ^{6} + 3} \frac{d}{d x} (x^{6} + 3)

\frac{d}{d x} (x^{6} + 3) = 6 x^{5}

= \frac{1}{ln ( 10 )} \cdot \frac{1}{x ^{6} + 3} \cdot 6 x^{5}

Simplify

\frac{1}{ln ( 10 )} \cdot \frac{1}{x ^{6} + 3} \cdot 6 x^{5} : \frac{6 x ^{5}}{ln ( 10 ) ( x ^{6} + 3 )}

= \frac{6 x ^{5}}{ln ( 10 ) ( x ^{6} + 3 )}

\int \frac{1}{y + 1} d y

\frac{sin ( t )}{4 + 4 cos ( t )}

\frac{\partial}{\partial x} (x^{2} + x y + y^{2} + y)

\int_{0}^{\frac{π}{2}} (sin (x))^{2} d x

e^{- 2 t} \cdot sin (t)

What is the derivative of log_{10}(x^6+3) ?
The derivative of log_{10}(x^6+3) is (6x^5)/(ln(10)(x^6+3))
What is the first derivative of log_{10}(x^6+3) ?
The first derivative of log_{10}(x^6+3) is (6x^5)/(ln(10)(x^6+3))