What is the derivative of 4/(sqrt(x+7)) ?

The derivative of 4/(sqrt(x+7)) is -2/(sqrt(x)(\sqrt{x)+7)^2}

What is the first derivative of 4/(sqrt(x+7)) ?

The first derivative of 4/(sqrt(x+7)) is -2/(sqrt(x)(\sqrt{x)+7)^2}

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\frac{d}{d x} (\frac{4}{x + 7})

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

Solution steps

\frac{d}{d x} (\frac{4}{x + 7})

Take the constant out:

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

= 4 \frac{d}{d x} (\frac{1}{x + 7})

Apply exponent rule:

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

= 4 \frac{d}{d x} ((x + 7)^{- 1})

Apply the chain rule:

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

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

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

= 4 (- \frac{1}{( x + 7 ) ^{2}} \cdot \frac{1}{2 x})

Simplify

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

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

\frac{d y}{d t} = 2 y - 1

y = \frac{2}{( x - 2 )}

\int_{0}^{6} π (x - 1)^{2} d x

\int \frac{1}{1 - x ^{2}} d x

x^{2} y^{^{'}} + 8 x y = 17 y^{3}

What is the derivative of 4/(sqrt(x+7)) ?
The derivative of 4/(sqrt(x+7)) is -2/(sqrt(x)(\sqrt{x)+7)^2}
What is the first derivative of 4/(sqrt(x+7)) ?
The first derivative of 4/(sqrt(x+7)) is -2/(sqrt(x)(\sqrt{x)+7)^2}