What is the derivative of log_{7}(x^2-7) ?

The derivative of log_{7}(x^2-7) is (2x)/(ln(7)(x^2-7))

What is the first derivative of log_{7}(x^2-7) ?

The first derivative of log_{7}(x^2-7) is (2x)/(ln(7)(x^2-7))

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\frac{d}{d x} (lo g_{7} (x^{2} - 7))

\frac{2 x}{ln ( 7 ) ( x ^{2} - 7 )}

Solution steps

\frac{d}{d x} (lo g_{7} (x^{2} - 7))

Apply log rule:

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

= \frac{d}{d x} (\frac{ln ( x ^{2} - 7 )}{ln ( 7 )})

Take the constant out:

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

= \frac{1}{ln ( 7 )} \frac{d}{d x} (ln (x^{2} - 7))

Apply the chain rule:

\frac{1}{x ^{2} - 7} \frac{d}{d x} (x^{2} - 7)

= \frac{1}{x ^{2} - 7} \frac{d}{d x} (x^{2} - 7)

\frac{d}{d x} (x^{2} - 7) = 2 x

= \frac{1}{ln ( 7 )} \cdot \frac{1}{x ^{2} - 7} \cdot 2 x

Simplify

\frac{1}{ln ( 7 )} \cdot \frac{1}{x ^{2} - 7} \cdot 2 x : \frac{2 x}{ln ( 7 ) ( x ^{2} - 7 )}

= \frac{2 x}{ln ( 7 ) ( x ^{2} - 7 )}

f (x) = 4 x^{4} - 3 x^{\frac{5}{2}} + 2

\frac{\partial}{\partial x} (3 e^{y} + x + x^{3} + 6)

\frac{( 3 s + 2 )}{s ^{2} + 4 s + 20}

\frac{d}{d x} (sin^{2} (x) cos (x))

y^{^{'}} = 2 x y^{2}

What is the derivative of log_{7}(x^2-7) ?
The derivative of log_{7}(x^2-7) is (2x)/(ln(7)(x^2-7))
What is the first derivative of log_{7}(x^2-7) ?
The first derivative of log_{7}(x^2-7) is (2x)/(ln(7)(x^2-7))