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Popular >

derivative of (x^2/(5+4x))

Solution

\frac{d}{d x} (\frac{x ^{2}}{5 + 4 x})

Solution

\frac{10 x + 4 x ^{2}}{( 5 + 4 x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{2}}{5 + 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} ) ( 5 + 4 x ) - \frac{d}{d x} ( 5 + 4 x ) x ^{2}}{( 5 + 4 x ) ^{2}}

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

\frac{d}{d x} (5 + 4 x) = 4

= \frac{2 x ( 5 + 4 x ) - 4 x ^{2}}{( 5 + 4 x ) ^{2}}

Expand

2 x (5 + 4 x) - 4 x^{2} : 10 x + 4 x^{2}

= \frac{10 x + 4 x ^{2}}{( 5 + 4 x ) ^{2}}

Popular Examples

(x^2+1)y^'+4x(y-1)=0,y(0)=5

(x^{2} + 1) y^{^{'}} + 4 x (y - 1) = 0, y (0) = 5

integral of xsqrt(16-25x^2)

\int x 16 - 25 x^{2} d x

integral from 0 to pi/2 of 3cos(x)

\int_{0}^{\frac{π}{2}} 3 cos (x) d x

derivative of f(x)=(3x^3+2x)(x-2)(x+4)derivative of

f (x) = (3 x^{3} + 2 x) (x - 2) (x + 4)

integral of 1/((4x^2-25)^{3/2)}

\int \frac{1}{( 4 x ^{2} - 25 ) ^{\frac{3}{2}}} d x

Frequently Asked Questions (FAQ)

What is the derivative of (x^2/(5+4x)) ?
The derivative of (x^2/(5+4x)) is (10x+4x^2)/((5+4x)^2)
What is the first derivative of (x^2/(5+4x)) ?
The first derivative of (x^2/(5+4x)) is (10x+4x^2)/((5+4x)^2)