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

The derivative of sqrt(5x^3-10x^2-3/x) is (15x^4-20x^3+3)/(2x^{3/2)sqrt(5x^4-10x^3-3)}

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

The first derivative of sqrt(5x^3-10x^2-3/x) is (15x^4-20x^3+3)/(2x^{3/2)sqrt(5x^4-10x^3-3)}

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derivative of

5 x^{3} - 10 x^{2} - \frac{3}{x}

\frac{15 x ^{4} - 20 x ^{3} + 3}{2 x ^{\frac{3}{2}} 5 x ^{4} - 10 x ^{3} - 3}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (5 x^{3} - 10 x^{2} - \frac{3}{x}) = 15 x^{2} - 20 x + \frac{3}{x ^{2}}

= \frac{1}{2 5 x ^{3} - 10 x ^{2} - \frac{3}{x}} (15 x^{2} - 20 x + \frac{3}{x ^{2}})

Simplify

\frac{1}{2 5 x ^{3} - 10 x ^{2} - \frac{3}{x}} (15 x^{2} - 20 x + \frac{3}{x ^{2}}) : \frac{15 x ^{4} - 20 x ^{3} + 3}{2 x ^{\frac{3}{2}} 5 x ^{4} - 10 x ^{3} - 3}

= \frac{15 x ^{4} - 20 x ^{3} + 3}{2 x ^{\frac{3}{2}} 5 x ^{4} - 10 x ^{3} - 3}

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

\frac{d y}{d t} = 5 y + y^{4}, y (0) = 1

1 - cos^{2} (17 x)

f (x) = 6 x^{2} - 20 x^{3}

\frac{d}{d x} (5 - ∣ x - 2 ∣)

What is the derivative of sqrt(5x^3-10x^2-3/x) ?
The derivative of sqrt(5x^3-10x^2-3/x) is (15x^4-20x^3+3)/(2x^{3/2)sqrt(5x^4-10x^3-3)}
What is the first derivative of sqrt(5x^3-10x^2-3/x) ?
The first derivative of sqrt(5x^3-10x^2-3/x) is (15x^4-20x^3+3)/(2x^{3/2)sqrt(5x^4-10x^3-3)}