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

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

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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

x 16 - x^{2}

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

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d x}{d x} = 1

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

= 1 \cdot 16 - x^{2} + (- \frac{x}{16 - x ^{2}}) x

Simplify

1 \cdot 16 - x^{2} + (- \frac{x}{16 - x ^{2}}) x : \frac{- 2 x ^{2} + 16}{16 - x ^{2}}

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

x \frac{d y}{d x} - y = x^{2} y^{2}

\int 24 sin (x) d x

d er i v a t i v e (2 x - 1)^{2}

\int 3 x e^{3 x} d x

\int_{- \infty}^{0} \frac{1}{3 - 4 x} d x

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