What is the derivative of (x^6+1^{5/2}) ?

The derivative of (x^6+1^{5/2}) is 15x^5(x^6+1)^{3/2}

What is the first derivative of (x^6+1^{5/2}) ?

The first derivative of (x^6+1^{5/2}) is 15x^5(x^6+1)^{3/2}

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Popular >

\frac{d}{d x} ((x^{6} + 1)^{\frac{5}{2}})

15 x^{5} (x^{6} + 1)^{\frac{3}{2}}

Solution steps

\frac{d}{d x} ((x^{6} + 1)^{\frac{5}{2}})

Apply the chain rule:

\frac{5 ( x ^{6} + 1 ) ^{\frac{3}{2}}}{2} \frac{d}{d x} (x^{6} + 1)

= \frac{5 ( x ^{6} + 1 ) ^{\frac{3}{2}}}{2} \frac{d}{d x} (x^{6} + 1)

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

= \frac{5 ( x ^{6} + 1 ) ^{\frac{3}{2}}}{2} \cdot 6 x^{5}

Simplify

\frac{5 ( x ^{6} + 1 ) ^{\frac{3}{2}}}{2} \cdot 6 x^{5} : 15 x^{5} (x^{6} + 1)^{\frac{3}{2}}

= 15 x^{5} (x^{6} + 1)^{\frac{3}{2}}

\int tan^{3} (x) sec^{4} (x) d x

t^{\frac{3}{2}} \cdot e^{- 2 t}

\frac{\partial}{\partial s} (\frac{t}{s})

\int_{0}^{1} \frac{x ^{3}}{x ^{2} + 1} d x

\int \frac{1}{5} x d x

What is the derivative of (x^6+1^{5/2}) ?
The derivative of (x^6+1^{5/2}) is 15x^5(x^6+1)^{3/2}
What is the first derivative of (x^6+1^{5/2}) ?
The first derivative of (x^6+1^{5/2}) is 15x^5(x^6+1)^{3/2}