What is the derivative of \sqrt[3]{8x^7+9x^6} ?

The derivative of \sqrt[3]{8x^7+9x^6} is (2x(28x+27))/(3(8x+9)^{2/3)}

What is the first derivative of \sqrt[3]{8x^7+9x^6} ?

The first derivative of \sqrt[3]{8x^7+9x^6} is (2x(28x+27))/(3(8x+9)^{2/3)}

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\frac{2 x ( 28 x + 27 )}{3 ( 8 x + 9 ) ^{\frac{2}{3}}}

Solution steps

Apply the chain rule:

\frac{1}{3 ( 8 x ^{7} + 9 x ^{6} ) ^{\frac{2}{3}}} \frac{d}{d x} (8 x^{7} + 9 x^{6})

= \frac{1}{3 ( 8 x ^{7} + 9 x ^{6} ) ^{\frac{2}{3}}} \frac{d}{d x} (8 x^{7} + 9 x^{6})

\frac{d}{d x} (8 x^{7} + 9 x^{6}) = 56 x^{6} + 54 x^{5}

= \frac{1}{3 ( 8 x ^{7} + 9 x ^{6} ) ^{\frac{2}{3}}} (56 x^{6} + 54 x^{5})

Simplify

\frac{1}{3 ( 8 x ^{7} + 9 x ^{6} ) ^{\frac{2}{3}}} (56 x^{6} + 54 x^{5}) : \frac{2 x ( 28 x + 27 )}{3 ( 8 x + 9 ) ^{\frac{2}{3}}}

= \frac{2 x ( 28 x + 27 )}{3 ( 8 x + 9 ) ^{\frac{2}{3}}}

\int \frac{1}{x ^{2} - 4 x + 4} d x

x \to 9 - lim (\frac{6 x}{x - 9})

\frac{d}{d x} (\frac{e ^{4 x}}{x})

\frac{d}{d t} (e^{a t})

\frac{6 x + 4 x ^{2}}{( 3 + 4 x ) ^{2}}

What is the derivative of \sqrt[3]{8x^7+9x^6} ?
The derivative of \sqrt[3]{8x^7+9x^6} is (2x(28x+27))/(3(8x+9)^{2/3)}
What is the first derivative of \sqrt[3]{8x^7+9x^6} ?
The first derivative of \sqrt[3]{8x^7+9x^6} is (2x(28x+27))/(3(8x+9)^{2/3)}