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

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

im pl i c i t \frac{d y}{d x}, x^{2} + y^{2} = 25

\frac{d x}{d t} = 4 x t^{5}

d er i v a t i v e \frac{x + 2}{x ^{3} + x - 6}

x \to 14 lim (x + 2)

d er i v a t i v e g (x) = ln (x e^{- 9 x})

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