What is the derivative of (2x^6+5x^3^{3/5}) ?

The derivative of (2x^6+5x^3^{3/5}) is (3(12x^5+15x^2))/(5(2x^6+5x^3)^{2/5)}

What is the first derivative of (2x^6+5x^3^{3/5}) ?

The first derivative of (2x^6+5x^3^{3/5}) is (3(12x^5+15x^2))/(5(2x^6+5x^3)^{2/5)}

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\frac{d}{d x} ((2 x^{6} + 5 x^{3})^{\frac{3}{5}})

\frac{3 ( 12 x ^{5} + 15 x ^{2} )}{5 ( 2 x ^{6} + 5 x ^{3} ) ^{\frac{2}{5}}}

Solution steps

\frac{d}{d x} ((2 x^{6} + 5 x^{3})^{\frac{3}{5}})

Apply the chain rule:

\frac{3}{5 ( 2 x ^{6} + 5 x ^{3} ) ^{\frac{2}{5}}} \frac{d}{d x} (2 x^{6} + 5 x^{3})

= \frac{3}{5 ( 2 x ^{6} + 5 x ^{3} ) ^{\frac{2}{5}}} \frac{d}{d x} (2 x^{6} + 5 x^{3})

\frac{d}{d x} (2 x^{6} + 5 x^{3}) = 12 x^{5} + 15 x^{2}

= \frac{3}{5 ( 2 x ^{6} + 5 x ^{3} ) ^{\frac{2}{5}}} (12 x^{5} + 15 x^{2})

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{3 ( 12 x ^{5} + 15 x ^{2} )}{5 ( 2 x ^{6} + 5 x ^{3} ) ^{\frac{2}{5}}}

What is the derivative of (2x^6+5x^3^{3/5}) ?
The derivative of (2x^6+5x^3^{3/5}) is (3(12x^5+15x^2))/(5(2x^6+5x^3)^{2/5)}
What is the first derivative of (2x^6+5x^3^{3/5}) ?
The first derivative of (2x^6+5x^3^{3/5}) is (3(12x^5+15x^2))/(5(2x^6+5x^3)^{2/5)}