What is the derivative of (5x^3+8x-3^{3/2}) ?

The derivative of (5x^3+8x-3^{3/2}) is (3(15x^2+8)(5x^3+8x-3)^{1/2})/2

What is the first derivative of (5x^3+8x-3^{3/2}) ?

The first derivative of (5x^3+8x-3^{3/2}) is (3(15x^2+8)(5x^3+8x-3)^{1/2})/2

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\frac{d}{d x} ((5 x^{3} + 8 x - 3)^{\frac{3}{2}})

\frac{3 ( 15 x ^{2} + 8 ) ( 5 x ^{3} + 8 x - 3 ) ^{\frac{1}{2}}}{2}

Solution steps

\frac{d}{d x} ((5 x^{3} + 8 x - 3)^{\frac{3}{2}})

Apply the chain rule:

\frac{3 ( 5 x ^{3} + 8 x - 3 ) ^{\frac{1}{2}}}{2} \frac{d}{d x} (5 x^{3} + 8 x - 3)

= \frac{3 ( 5 x ^{3} + 8 x - 3 ) ^{\frac{1}{2}}}{2} \frac{d}{d x} (5 x^{3} + 8 x - 3)

\frac{d}{d x} (5 x^{3} + 8 x - 3) = 15 x^{2} + 8

= \frac{3 ( 5 x ^{3} + 8 x - 3 ) ^{\frac{1}{2}}}{2} (15 x^{2} + 8)

Multiply fractions:

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

= \frac{3 ( 15 x ^{2} + 8 ) ( 5 x ^{3} + 8 x - 3 ) ^{\frac{1}{2}}}{2}

What is the derivative of (5x^3+8x-3^{3/2}) ?
The derivative of (5x^3+8x-3^{3/2}) is (3(15x^2+8)(5x^3+8x-3)^{1/2})/2
What is the first derivative of (5x^3+8x-3^{3/2}) ?
The first derivative of (5x^3+8x-3^{3/2}) is (3(15x^2+8)(5x^3+8x-3)^{1/2})/2