What is the derivative of y= 3/(sqrt(x+7)) ?

The derivative of y= 3/(sqrt(x+7)) is -3/(2(x+7)^{3/2)}

What is the first derivative of y= 3/(sqrt(x+7)) ?

The first derivative of y= 3/(sqrt(x+7)) is -3/(2(x+7)^{3/2)}

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derivative of

y = \frac{3}{x + 7}

- \frac{3}{2 ( x + 7 ) ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (\frac{3}{x + 7})

Take the constant out:

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

= 3 \frac{d}{d x} (\frac{1}{x + 7})

Apply exponent rule:

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

= 3 \frac{d}{d x} ((x + 7)^{- \frac{1}{2}})

Apply the chain rule:

- \frac{1}{2 ( x + 7 ) ^{\frac{3}{2}}} \frac{d}{d x} (x + 7)

= - \frac{1}{2 ( x + 7 ) ^{\frac{3}{2}}} \frac{d}{d x} (x + 7)

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

= 3 (- \frac{1}{2 ( x + 7 ) ^{\frac{3}{2}}} \cdot 1)

Simplify

3 (- \frac{1}{2 ( x + 7 ) ^{\frac{3}{2}}} \cdot 1) : - \frac{3}{2 ( x + 7 ) ^{\frac{3}{2}}}

= - \frac{3}{2 ( x + 7 ) ^{\frac{3}{2}}}

\int \frac{1}{16 - 49 x ^{2}} d x

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

\int \frac{1}{( y + 2 ) ^{2}} d y

\frac{d y}{d x} + 3 x^{2} y = x

x \to 1 lim (x^{4} - x^{2} + 2)

What is the derivative of y= 3/(sqrt(x+7)) ?
The derivative of y= 3/(sqrt(x+7)) is -3/(2(x+7)^{3/2)}
What is the first derivative of y= 3/(sqrt(x+7)) ?
The first derivative of y= 3/(sqrt(x+7)) is -3/(2(x+7)^{3/2)}