What is the derivative of (x^2-9x+9)sqrt(25-x^2) ?

The derivative of (x^2-9x+9)sqrt(25-x^2) is (-3x^3+18x^2+41x-225)/(sqrt(25-x^2))

What is the first derivative of (x^2-9x+9)sqrt(25-x^2) ?

The first derivative of (x^2-9x+9)sqrt(25-x^2) is (-3x^3+18x^2+41x-225)/(sqrt(25-x^2))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

(x^{2} - 9 x + 9) 25 - x^{2}

\frac{- 3 x ^{3} + 18 x ^{2} + 41 x - 225}{25 - x ^{2}}

Solution steps

\frac{d}{d x} ((x^{2} - 9 x + 9) 25 - x^{2})

Apply the Product Rule:

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

f = x^{2} - 9 x + 9, g = 25 - x^{2}

= \frac{d}{d x} (x^{2} - 9 x + 9) 25 - x^{2} + \frac{d}{d x} (25 - x^{2}) (x^{2} - 9 x + 9)

\frac{d}{d x} (x^{2} - 9 x + 9) = 2 x - 9

\frac{d}{d x} (25 - x^{2}) = - \frac{x}{25 - x ^{2}}

= (2 x - 9) 25 - x^{2} + (- \frac{x}{25 - x ^{2}}) (x^{2} - 9 x + 9)

Simplify

(2 x - 9) 25 - x^{2} + (- \frac{x}{25 - x ^{2}}) (x^{2} - 9 x + 9) : \frac{- 3 x ^{3} + 18 x ^{2} + 41 x - 225}{25 - x ^{2}}

= \frac{- 3 x ^{3} + 18 x ^{2} + 41 x - 225}{25 - x ^{2}}

x \to 0 lim (\frac{( 3 ^{x} - 2 ^{x} )}{x})

\int (e^{2 x} + e^{- 3 x}) d x

(ln (x))^{5}

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

r \to \infty lim (ln (r))

What is the derivative of (x^2-9x+9)sqrt(25-x^2) ?
The derivative of (x^2-9x+9)sqrt(25-x^2) is (-3x^3+18x^2+41x-225)/(sqrt(25-x^2))
What is the first derivative of (x^2-9x+9)sqrt(25-x^2) ?
The first derivative of (x^2-9x+9)sqrt(25-x^2) is (-3x^3+18x^2+41x-225)/(sqrt(25-x^2))