What is the derivative of 4/5 ln((9x^2-6^7)) ?

The derivative of 4/5 ln((9x^2-6^7)) is (168x)/(5(3x^2-2))

What is the first derivative of 4/5 ln((9x^2-6^7)) ?

The first derivative of 4/5 ln((9x^2-6^7)) is (168x)/(5(3x^2-2))

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\frac{d}{d x} (\frac{4}{5} ln ((9 x^{2} - 6)^{7}))

\frac{168 x}{5 ( 3 x ^{2} - 2 )}

Solution steps

\frac{d}{d x} (\frac{4}{5} ln ((9 x^{2} - 6)^{7}))

Take the constant out:

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

= \frac{4}{5} \frac{d}{d x} (ln ((9 x^{2} - 6)^{7}))

Apply the chain rule:

\frac{1}{( 9 x ^{2} - 6 ) ^{7}} \frac{d}{d x} ((9 x^{2} - 6)^{7})

= \frac{1}{( 9 x ^{2} - 6 ) ^{7}} \frac{d}{d x} ((9 x^{2} - 6)^{7})

\frac{d}{d x} ((9 x^{2} - 6)^{7}) = 126 x (9 x^{2} - 6)^{6}

= \frac{4}{5} \cdot \frac{1}{( 9 x ^{2} - 6 ) ^{7}} \cdot 126 x (9 x^{2} - 6)^{6}

Simplify

\frac{4}{5} \cdot \frac{1}{( 9 x ^{2} - 6 ) ^{7}} \cdot 126 x (9 x^{2} - 6)^{6} : \frac{168 x}{5 ( 3 x ^{2} - 2 )}

= \frac{168 x}{5 ( 3 x ^{2} - 2 )}

\int_{2}^{4} \frac{( 2 x - 3 )}{6} d x

x \to 2 lim (x^{2} - x)

x \to \infty lim (\frac{7 ^{12} - 2176782336}{7 ^{11}})

\int \frac{x ^{2}}{( 1 - 4 x ^{2} ) ^{\frac{3}{2}}} d x

\int_{0}^{1} e^{2 x} - e^{x} d x

What is the derivative of 4/5 ln((9x^2-6^7)) ?
The derivative of 4/5 ln((9x^2-6^7)) is (168x)/(5(3x^2-2))
What is the first derivative of 4/5 ln((9x^2-6^7)) ?
The first derivative of 4/5 ln((9x^2-6^7)) is (168x)/(5(3x^2-2))