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Popular >

derivative of y=\sqrt[5]{x^4}

Solution

derivative of

Solution

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

Solution steps

Apply the chain rule:

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

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

\frac{d}{d x} (x^{4}) = 4 x^{3}

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

Simplify

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

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

Popular Examples

implicit ln(xy^9)=xy implicit derivative

ln (x y^{9}) = x y

integral of (x^3)/(27)-4/9 x^2+4/3 x+1

\int \frac{x ^{3}}{27} - \frac{4}{9} x^{2} + \frac{4}{3} x + 1 d x

derivative of-3/(sqrt(x^5))

\frac{d}{d x} (- \frac{3}{x ^{5}})

xy^'+y=(xy)^{3/2}

x y^{^{'}} + y = (x y)^{\frac{3}{2}}

integral from-9 to 0 of 2+sqrt(81-x^2)

\int_{- 9}^{0} 2 + 81 - x^{2} d x

Frequently Asked Questions (FAQ)

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