What is the derivative of \sqrt[4]{x^5+6x} ?

The derivative of \sqrt[4]{x^5+6x} is (5x^4+6)/(4(x^5+6x)^{3/4)}

What is the first derivative of \sqrt[4]{x^5+6x} ?

The first derivative of \sqrt[4]{x^5+6x} is (5x^4+6)/(4(x^5+6x)^{3/4)}

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derivative of

\frac{5 x ^{4} + 6}{4 ( x ^{5} + 6 x ) ^{\frac{3}{4}}}

Solution steps

Apply the chain rule:

\frac{1}{4 ( x ^{5} + 6 x ) ^{\frac{3}{4}}} \frac{d}{d x} (x^{5} + 6 x)

= \frac{1}{4 ( x ^{5} + 6 x ) ^{\frac{3}{4}}} \frac{d}{d x} (x^{5} + 6 x)

\frac{d}{d x} (x^{5} + 6 x) = 5 x^{4} + 6

= \frac{1}{4 ( x ^{5} + 6 x ) ^{\frac{3}{4}}} (5 x^{4} + 6)

Simplify

\frac{1}{4 ( x ^{5} + 6 x ) ^{\frac{3}{4}}} (5 x^{4} + 6) : \frac{5 x ^{4} + 6}{4 ( x ^{5} + 6 x ) ^{\frac{3}{4}}}

= \frac{5 x ^{4} + 6}{4 ( x ^{5} + 6 x ) ^{\frac{3}{4}}}

e^{3 t}

x \to 2 lim (x 4 - x^{2})

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

\frac{d}{d x} (2 x^{3} - 15 x^{2} + 36 x + 5)

x^{2} - x, 3 x + 5

What is the derivative of \sqrt[4]{x^5+6x} ?
The derivative of \sqrt[4]{x^5+6x} is (5x^4+6)/(4(x^5+6x)^{3/4)}
What is the first derivative of \sqrt[4]{x^5+6x} ?
The first derivative of \sqrt[4]{x^5+6x} is (5x^4+6)/(4(x^5+6x)^{3/4)}