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Popular >

derivative of (x+1/(x+5))

Solution

\frac{d}{d x} (\frac{x + 1}{x + 5})

Solution

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

Solution steps

\frac{d}{d x} (\frac{x + 1}{x + 5})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x + 1 ) ( x + 5 ) - \frac{d}{d x} ( x + 5 ) ( x + 1 )}{( x + 5 ) ^{2}}

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

\frac{d}{d x} (x + 5) = 1

= \frac{1 \cdot ( x + 5 ) - 1 \cdot ( x + 1 )}{( x + 5 ) ^{2}}

Simplify

\frac{1 \cdot ( x + 5 ) - 1 \cdot ( x + 1 )}{( x + 5 ) ^{2}} : \frac{4}{( x + 5 ) ^{2}}

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

Popular Examples

y^{''}-8y^'+25y=208sin(3x)

y^{^{''}} - 8 y^{^{'}} + 25 y = 208 sin (3 x)

y^'=(2xy)/(x^2-y^2)

y^{^{'}} = \frac{2 x y}{x ^{2} - y ^{2}}

area 4x=4y-y^2,4x-y=0 area

4 x = 4 y - y^{2}, 4 x - y = 0

integral of 1/(x^2sqrt(7+x^2))

\int \frac{1}{x ^{2} 7 + x ^{2}} d x

derivative of f(x)=e^{7x}cos(10x)derivative of

f (x) = e^{7 x} cos (10 x)

Frequently Asked Questions (FAQ)

What is the derivative of (x+1/(x+5)) ?
The derivative of (x+1/(x+5)) is 4/((x+5)^2)
What is the first derivative of (x+1/(x+5)) ?
The first derivative of (x+1/(x+5)) is 4/((x+5)^2)