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

The derivative of \sqrt[5]{x}+6sqrt(x^5) is (1+75x^{23/10})/(5x^{4/5)}

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

The first derivative of \sqrt[5]{x}+6sqrt(x^5) is (1+75x^{23/10})/(5x^{4/5)}

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

\frac{1 + 75 x ^{\frac{23}{10}}}{5 x ^{\frac{4}{5}}}

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

= \frac{1}{5 x ^{\frac{4}{5}}} + 15 x^{\frac{3}{2}}

Simplify

\frac{1}{5 x ^{\frac{4}{5}}} + 15 x^{\frac{3}{2}} : \frac{1 + 75 x ^{\frac{23}{10}}}{5 x ^{\frac{4}{5}}}

= \frac{1 + 75 x ^{\frac{23}{10}}}{5 x ^{\frac{4}{5}}}

x \to - 8 lim (- 4 x)

e^{- x} x

y^{^{'}} = \frac{( x ^{4} y ^{4} + x ^{4} )}{y ^{3}}

\frac{\partial}{\partial y} (\frac{( x ^{2} )}{y ^{3}})

\int \frac{sin ( x )}{2 + cos ^{2} ( x )} d x

What is the derivative of \sqrt[5]{x}+6sqrt(x^5) ?
The derivative of \sqrt[5]{x}+6sqrt(x^5) is (1+75x^{23/10})/(5x^{4/5)}
What is the first derivative of \sqrt[5]{x}+6sqrt(x^5) ?
The first derivative of \sqrt[5]{x}+6sqrt(x^5) is (1+75x^{23/10})/(5x^{4/5)}