What is the derivative of (5x^2+11x)^{4/3} ?

The derivative of (5x^2+11x)^{4/3} is (4(10x+11)(5x^2+11x)^{1/3})/3

What is the first derivative of (5x^2+11x)^{4/3} ?

The first derivative of (5x^2+11x)^{4/3} is (4(10x+11)(5x^2+11x)^{1/3})/3

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derivative of

(5 x^{2} + 11 x)^{\frac{4}{3}}

\frac{4 ( 10 x + 11 ) ( 5 x ^{2} + 11 x ) ^{\frac{1}{3}}}{3}

Solution steps

\frac{d}{d x} ((5 x^{2} + 11 x)^{\frac{4}{3}})

Apply the chain rule:

\frac{4 ( 5 x ^{2} + 11 x ) ^{\frac{1}{3}}}{3} \frac{d}{d x} (5 x^{2} + 11 x)

= \frac{4 ( 5 x ^{2} + 11 x ) ^{\frac{1}{3}}}{3} \frac{d}{d x} (5 x^{2} + 11 x)

\frac{d}{d x} (5 x^{2} + 11 x) = 10 x + 11

= \frac{4 ( 5 x ^{2} + 11 x ) ^{\frac{1}{3}}}{3} (10 x + 11)

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{4 ( 10 x + 11 ) ( 5 x ^{2} + 11 x ) ^{\frac{1}{3}}}{3}

\int e^{- x (y + 1)} d x

\int_{0}^{50} 9.8 (500 - 10 y) d y

\frac{\partial}{\partial t} (2 t)

f (x) = \frac{6}{4 x + 1}, at x = - 1

3 x^{5} - 3 x^{4} + x^{3}

What is the derivative of (5x^2+11x)^{4/3} ?
The derivative of (5x^2+11x)^{4/3} is (4(10x+11)(5x^2+11x)^{1/3})/3
What is the first derivative of (5x^2+11x)^{4/3} ?
The first derivative of (5x^2+11x)^{4/3} is (4(10x+11)(5x^2+11x)^{1/3})/3