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Popular >

derivative of 7/(x+1)

Solution

\frac{d}{d x} (\frac{7}{x + 1})

Solution

- \frac{7}{( x + 1 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{7}{x + 1})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 7 \frac{d}{d x} (\frac{1}{x + 1})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= 7 \frac{d}{d x} ((x + 1)^{- 1})

Apply the chain rule:

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

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

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

= 7 (- \frac{1}{( x + 1 ) ^{2}} \cdot 1)

Simplify

7 (- \frac{1}{( x + 1 ) ^{2}} \cdot 1) : - \frac{7}{( x + 1 ) ^{2}}

= - \frac{7}{( x + 1 ) ^{2}}

Popular Examples

derivative of x^2ln(x/4)

\frac{d}{d x} (x^{2} ln (\frac{x}{4}))

derivative of 6x^4(x^2-7x)

\frac{d}{d x} (6 x^{4} (x^{2} - 7 x))

integral from 0 to pi/2 of 17cos^5(x)

\int_{0}^{\frac{π}{2}} 17 cos^{5} (x) d x

integral of (2x)/(x^2-3x-10)

\int \frac{2 x}{x ^{2} - 3 x - 10} d x

(\partial)/(\partial y)(x^{1/2}*y^{1/2})

\frac{\partial}{\partial y} (x^{\frac{1}{2}} \cdot y^{\frac{1}{2}})

Frequently Asked Questions (FAQ)

What is the derivative of 7/(x+1) ?
The derivative of 7/(x+1) is -7/((x+1)^2)
What is the first derivative of 7/(x+1) ?
The first derivative of 7/(x+1) is -7/((x+1)^2)