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

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

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

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

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derivative of

5 t + 6 t^{5}

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

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

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

\frac{d}{d x} (x (1 - x))

y^{^{'}} + 2 y = 0

x \to \infty lim (7 + \frac{6}{x})

\frac{d y}{d x}, y = \frac{1}{x}

\int \frac{1}{( x - 1 )} d x

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