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Popular >

derivative of (x+2/(x+3))

Solution

\frac{d}{d x} (\frac{x + 2}{x + 3})

Solution

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

Solution steps

\frac{d}{d x} (\frac{x + 2}{x + 3})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x + 2 ) ( x + 3 ) - \frac{d}{d x} ( x + 3 ) ( x + 2 )}{( x + 3 ) ^{2}}

\frac{d}{d x} (x + 2) = 1

\frac{d}{d x} (x + 3) = 1

= \frac{1 \cdot ( x + 3 ) - 1 \cdot ( x + 2 )}{( x + 3 ) ^{2}}

Simplify

\frac{1 \cdot ( x + 3 ) - 1 \cdot ( x + 2 )}{( x + 3 ) ^{2}} : \frac{1}{( x + 3 ) ^{2}}

= \frac{1}{( x + 3 ) ^{2}}

Popular Examples

integral of 0.02

\int 0.02

integral of (sin(x))/(sqrt(7-cos^2(x)))

\int \frac{sin ( x )}{7 - cos ^{2} ( x )} d x

integral of (x^3-11x-26)/(x^2-2x-8)

\int \frac{x ^{3} - 11 x - 26}{x ^{2} - 2 x - 8} d x

integral of 1/(sin^4(3x)cos^2(3x))

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

d/(dy)((x+y)^2)

\frac{d}{d y} ((x + y)^{2})

Frequently Asked Questions (FAQ)

What is the derivative of (x+2/(x+3)) ?
The derivative of (x+2/(x+3)) is 1/((x+3)^2)
What is the first derivative of (x+2/(x+3)) ?
The first derivative of (x+2/(x+3)) is 1/((x+3)^2)