What is the derivative of x^2sqrt(16-x^2) ?

The derivative of x^2sqrt(16-x^2) is (-3x^3+32x)/(sqrt(16-x^2))

What is the first derivative of x^2sqrt(16-x^2) ?

The first derivative of x^2sqrt(16-x^2) is (-3x^3+32x)/(sqrt(16-x^2))

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derivative of

x^{2} 16 - x^{2}

\frac{- 3 x ^{3} + 32 x}{16 - x ^{2}}

Solution steps

\frac{d}{d x} (x^{2} 16 - x^{2})

Apply the Product Rule:

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

f = x^{2}, g = 16 - x^{2}

= \frac{d}{d x} (x^{2}) 16 - x^{2} + \frac{d}{d x} (16 - x^{2}) x^{2}

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

\frac{d}{d x} (16 - x^{2}) = - \frac{x}{16 - x ^{2}}

= 2 x 16 - x^{2} + (- \frac{x}{16 - x ^{2}}) x^{2}

Simplify

2 x 16 - x^{2} + (- \frac{x}{16 - x ^{2}}) x^{2} : \frac{- 3 x ^{3} + 32 x}{16 - x ^{2}}

= \frac{- 3 x ^{3} + 32 x}{16 - x ^{2}}

\frac{1}{s ^{2} - 2 s}

- \frac{8}{x ^{2}}

\int_{0}^{\infty} e^{x} d x

\int \frac{1}{1 + 49 x ^{2}} d x

\frac{\partial}{\partial y} (ln (x^{7} + y^{7}))

What is the derivative of x^2sqrt(16-x^2) ?
The derivative of x^2sqrt(16-x^2) is (-3x^3+32x)/(sqrt(16-x^2))
What is the first derivative of x^2sqrt(16-x^2) ?
The first derivative of x^2sqrt(16-x^2) is (-3x^3+32x)/(sqrt(16-x^2))