What is the derivative of (10-5x^2^{4/3}) ?

The derivative of (10-5x^2^{4/3}) is -(40x(10-5x^2)^{1/3})/3

What is the first derivative of (10-5x^2^{4/3}) ?

The first derivative of (10-5x^2^{4/3}) is -(40x(10-5x^2)^{1/3})/3

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\frac{d}{d x} ((10 - 5 x^{2})^{\frac{4}{3}})

- \frac{40 x ( 10 - 5 x ^{2} ) ^{\frac{1}{3}}}{3}

Solution steps

\frac{d}{d x} ((10 - 5 x^{2})^{\frac{4}{3}})

Apply the chain rule:

\frac{4 ( 10 - 5 x ^{2} ) ^{\frac{1}{3}}}{3} \frac{d}{d x} (10 - 5 x^{2})

= \frac{4 ( 10 - 5 x ^{2} ) ^{\frac{1}{3}}}{3} \frac{d}{d x} (10 - 5 x^{2})

\frac{d}{d x} (10 - 5 x^{2}) = - 10 x

= \frac{4 ( 10 - 5 x ^{2} ) ^{\frac{1}{3}}}{3} (- 10 x)

Simplify

\frac{4 ( 10 - 5 x ^{2} ) ^{\frac{1}{3}}}{3} (- 10 x) : - \frac{40 x ( 10 - 5 x ^{2} ) ^{\frac{1}{3}}}{3}

= - \frac{40 x ( 10 - 5 x ^{2} ) ^{\frac{1}{3}}}{3}

f (x) = 7 x - 7 x

n = 3 \sum \infty 2 n + 5

ln (x + 4 + e^{- 3 x})

What is the derivative of (10-5x^2^{4/3}) ?
The derivative of (10-5x^2^{4/3}) is -(40x(10-5x^2)^{1/3})/3
What is the first derivative of (10-5x^2^{4/3}) ?
The first derivative of (10-5x^2^{4/3}) is -(40x(10-5x^2)^{1/3})/3