en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of y=xsqrt(3600-x^2)

Solution

derivative of

y = x 3600 - x^{2}

Solution

\frac{- 2 x ^{2} + 3600}{3600 - x ^{2}}

Solution steps

\frac{d}{d x} (x 3600 - x^{2})

Apply the Product Rule:

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

f = x, g = 3600 - x^{2}

= \frac{d x}{d x} 3600 - x^{2} + \frac{d}{d x} (3600 - x^{2}) x

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

\frac{d}{d x} (3600 - x^{2}) = - \frac{x}{3600 - x ^{2}}

= 1 \cdot 3600 - x^{2} + (- \frac{x}{3600 - x ^{2}}) x

Simplify

1 \cdot 3600 - x^{2} + (- \frac{x}{3600 - x ^{2}}) x : \frac{- 2 x ^{2} + 3600}{3600 - x ^{2}}

= \frac{- 2 x ^{2} + 3600}{3600 - x ^{2}}

Popular Examples

derivative of 2t^3cos(t)derivative of

2 t^{3} cos (t)

(\partial)/(\partial z)(e^{xyz^2+z})

\frac{\partial}{\partial z} (e^{x y z^{2} + z})

integral from 0 to pi/4 of sin^5(2x)

\int_{0}^{\frac{π}{4}} sin^{5} (2 x) d x

(\partial)/(\partial x)(4x^2+4y^3)

\frac{\partial}{\partial x} (4 x^{2} + 4 y^{3})

limit as x approaches infinity of (((a^{(1/x)}+b^{(1/x)})^x))/(2^x)

x \to \infty lim \frac{( ( a ^{(\frac{1}{x})} + b ^{(\frac{1}{x})} ) ^{x} )}{2 ^{x}}

Frequently Asked Questions (FAQ)

What is the derivative of y=xsqrt(3600-x^2) ?
The derivative of y=xsqrt(3600-x^2) is (-2x^2+3600)/(sqrt(3600-x^2))
What is the first derivative of y=xsqrt(3600-x^2) ?
The first derivative of y=xsqrt(3600-x^2) is (-2x^2+3600)/(sqrt(3600-x^2))