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

The derivative of (5x^2-3x^5/(-sqrt(x))) is -(3sqrt(x)(-3x^3+5))/2+9x^{7/2}

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

The first derivative of (5x^2-3x^5/(-sqrt(x))) is -(3sqrt(x)(-3x^3+5))/2+9x^{7/2}

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

- \frac{3 x ( - 3 x ^{3} + 5 )}{2} + 9 x^{\frac{7}{2}}

Solution steps

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

Simplify

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

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{\frac{3}{2}}, g = - 3 x^{3} + 5

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

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

\frac{d}{d x} (- 3 x^{3} + 5) = - 9 x^{2}

= - (\frac{3 x}{2} (- 3 x^{3} + 5) + (- 9 x^{2}) x^{\frac{3}{2}})

Simplify

- (\frac{3 x}{2} (- 3 x^{3} + 5) + (- 9 x^{2}) x^{\frac{3}{2}}) : - \frac{3 x ( - 3 x ^{3} + 5 )}{2} + 9 x^{\frac{7}{2}}

= - \frac{3 x ( - 3 x ^{3} + 5 )}{2} + 9 x^{\frac{7}{2}}

\int_{- \infty}^{\infty} x d x

\int e^{- 2 x} (x^{2} - 3 x + 4) d x

\frac{s}{s ^{2} - 2 s + 5}

(8 - 2 x^{3})^{3}

\int \frac{1}{x 9 + x ^{2}} d x

What is the derivative of (5x^2-3x^5/(-sqrt(x))) ?
The derivative of (5x^2-3x^5/(-sqrt(x))) is -(3sqrt(x)(-3x^3+5))/2+9x^{7/2}
What is the first derivative of (5x^2-3x^5/(-sqrt(x))) ?
The first derivative of (5x^2-3x^5/(-sqrt(x))) is -(3sqrt(x)(-3x^3+5))/2+9x^{7/2}