en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of f(x)=(x^2)/(9+4x)

Solution

derivative of

f (x) = \frac{x ^{2}}{9 + 4 x}

Solution

\frac{18 x + 4 x ^{2}}{( 9 + 4 x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{2}}{9 + 4 x})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( x ^{2} ) ( 9 + 4 x ) - \frac{d}{d x} ( 9 + 4 x ) x ^{2}}{( 9 + 4 x ) ^{2}}

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

\frac{d}{d x} (9 + 4 x) = 4

= \frac{2 x ( 9 + 4 x ) - 4 x ^{2}}{( 9 + 4 x ) ^{2}}

Expand

2 x (9 + 4 x) - 4 x^{2} : 18 x + 4 x^{2}

= \frac{18 x + 4 x ^{2}}{( 9 + 4 x ) ^{2}}

Popular Examples

integral of 5/(sin(x))

\int \frac{5}{sin ( x )} d x

derivative of 4sqrt(2x^2+9)derivative of

4 2 x^{2} + 9

derivative of f(x)=-3x^5cos(x)derivative of

f (x) = - 3 x^{5} cos (x)

integral of (x^3)/((1+x^4)^{1/2)}

\int \frac{x ^{3}}{( 1 + x ^{4} ) ^{\frac{1}{2}}} d x

derivative of f(x)=x^{5/2}e^x derivative of

f (x) = x^{\frac{5}{2}} e^{x}

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=(x^2)/(9+4x) ?
The derivative of f(x)=(x^2)/(9+4x) is (18x+4x^2)/((9+4x)^2)
What is the first derivative of f(x)=(x^2)/(9+4x) ?
The first derivative of f(x)=(x^2)/(9+4x) is (18x+4x^2)/((9+4x)^2)