What is the derivative of f(x)=(2sin^3(x)-5x)^{5/3} ?

The derivative of f(x)=(2sin^3(x)-5x)^{5/3} is (5(6sin^2(x)cos(x)-5)(2sin^3(x)-5x)^{2/3})/3

What is the first derivative of f(x)=(2sin^3(x)-5x)^{5/3} ?

The first derivative of f(x)=(2sin^3(x)-5x)^{5/3} is (5(6sin^2(x)cos(x)-5)(2sin^3(x)-5x)^{2/3})/3

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derivative of

f (x) = (2 sin^{3} (x) - 5 x)^{\frac{5}{3}}

\frac{5 ( 6 sin ^{2} ( x ) cos ( x ) - 5 ) ( 2 sin ^{3} ( x ) - 5 x ) ^{\frac{2}{3}}}{3}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (2 sin^{3} (x) - 5 x) = 6 sin^{2} (x) cos (x) - 5

= \frac{5 ( 2 sin ^{3} ( x ) - 5 x ) ^{\frac{2}{3}}}{3} (6 sin^{2} (x) cos (x) - 5)

Multiply fractions:

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

= \frac{5 ( 6 sin ^{2} ( x ) cos ( x ) - 5 ) ( 2 sin ^{3} ( x ) - 5 x ) ^{\frac{2}{3}}}{3}

(3, - 5), (7, 9)

2 x \cdot e^{x^{2}}

f (x, y) = - e^{x - y^{2} + x y}

(15, 3), (2, - 14)

f (x) = x^{2} - 5

What is the derivative of f(x)=(2sin^3(x)-5x)^{5/3} ?
The derivative of f(x)=(2sin^3(x)-5x)^{5/3} is (5(6sin^2(x)cos(x)-5)(2sin^3(x)-5x)^{2/3})/3
What is the first derivative of f(x)=(2sin^3(x)-5x)^{5/3} ?
The first derivative of f(x)=(2sin^3(x)-5x)^{5/3} is (5(6sin^2(x)cos(x)-5)(2sin^3(x)-5x)^{2/3})/3