What is the derivative of \sqrt[3]{(x-3^3(x+5)}) ?

The derivative of \sqrt[3]{(x-3^3(x+5)}) is (4(x+3))/(3(x+5)^{2/3)}

What is the first derivative of \sqrt[3]{(x-3^3(x+5)}) ?

The first derivative of \sqrt[3]{(x-3^3(x+5)}) is (4(x+3))/(3(x+5)^{2/3)}

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\frac{4 ( x + 3 )}{3 ( x + 5 ) ^{\frac{2}{3}}}

Solution steps

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{3 ( ( x - 3 ) ^{3} ( x + 5 ) ) ^{\frac{2}{3}}} (3 (x - 3)^{2} (x + 5) + (x - 3)^{3}) : \frac{4 ( x + 3 )}{3 ( x + 5 ) ^{\frac{2}{3}}}

= \frac{4 ( x + 3 )}{3 ( x + 5 ) ^{\frac{2}{3}}}

\frac{\partial}{\partial y} (sin (x - y) + (x + y))

\frac{d y}{d x} = 6 y e^{x + 4}

t^{2} + 2 t - 3

\frac{\partial}{\partial x} (\frac{( x - y )}{x})

n = 1 \sum \infty \frac{2}{3 n + 9}

What is the derivative of \sqrt[3]{(x-3^3(x+5)}) ?
The derivative of \sqrt[3]{(x-3^3(x+5)}) is (4(x+3))/(3(x+5)^{2/3)}
What is the first derivative of \sqrt[3]{(x-3^3(x+5)}) ?
The first derivative of \sqrt[3]{(x-3^3(x+5)}) is (4(x+3))/(3(x+5)^{2/3)}