What is the derivative of ((10+x/pi)^{1/3}) ?

The derivative of ((10+x/pi)^{1/3}) is 1/(3pi^{1/3)(x+10)^{2/3}}

What is the first derivative of ((10+x/pi)^{1/3}) ?

The first derivative of ((10+x/pi)^{1/3}) is 1/(3pi^{1/3)(x+10)^{2/3}}

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\frac{d}{d x} ((\frac{10 + x}{π})^{\frac{1}{3}})

\frac{1}{3 π ^{\frac{1}{3}} ( x + 10 ) ^{\frac{2}{3}}}

Solution steps

\frac{d}{d x} ((\frac{10 + x}{π})^{\frac{1}{3}})

Apply the chain rule:

\frac{1}{3 ( \frac{10 + x}{π} ) ^{\frac{2}{3}}} \frac{d}{d x} (\frac{10 + x}{π})

= \frac{1}{3 ( \frac{10 + x}{π} ) ^{\frac{2}{3}}} \frac{d}{d x} (\frac{10 + x}{π})

\frac{d}{d x} (\frac{10 + x}{π}) = \frac{1}{π}

= \frac{1}{3 ( \frac{10 + x}{π} ) ^{\frac{2}{3}}} \cdot \frac{1}{π}

Simplify

\frac{1}{3 ( \frac{10 + x}{π} ) ^{\frac{2}{3}}} \cdot \frac{1}{π} : \frac{1}{3 π ^{\frac{1}{3}} ( x + 10 ) ^{\frac{2}{3}}}

= \frac{1}{3 π ^{\frac{1}{3}} ( x + 10 ) ^{\frac{2}{3}}}

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

\frac{\partial}{\partial x} (z \cdot arctan (\frac{y}{x}))

\int_{2}^{\infty} \frac{8 cos ( \frac{π}{x} )}{x ^{2}} d x

h \to + 0 lim (\frac{\frac{1}{a + h} - \frac{1}{a}}{h})

\frac{d}{d t} (t)

What is the derivative of ((10+x/pi)^{1/3}) ?
The derivative of ((10+x/pi)^{1/3}) is 1/(3pi^{1/3)(x+10)^{2/3}}
What is the first derivative of ((10+x/pi)^{1/3}) ?
The first derivative of ((10+x/pi)^{1/3}) is 1/(3pi^{1/3)(x+10)^{2/3}}