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}}

\frac{d y}{d x}, x^{2} + y^{2} = 25

x \to 2 lim ([g (x)]^{3})

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

, (x + 3)^{11}

2 x^{2} - 3 x, at x = 4

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))