What is the derivative of 1/(2sqrt(x+10)) ?

The derivative of 1/(2sqrt(x+10)) is -1/(4(x+10)^{3/2)}

What is the first derivative of 1/(2sqrt(x+10)) ?

The first derivative of 1/(2sqrt(x+10)) is -1/(4(x+10)^{3/2)}

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derivative of

\frac{1}{2 x + 10}

- \frac{1}{4 ( x + 10 ) ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (\frac{1}{2 x + 10})

Take the constant out:

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

= \frac{1}{2} \frac{d}{d x} (\frac{1}{x + 10})

Apply exponent rule:

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

= \frac{1}{2} \frac{d}{d x} ((x + 10)^{- \frac{1}{2}})

Apply the chain rule:

- \frac{1}{2 ( x + 10 ) ^{\frac{3}{2}}} \frac{d}{d x} (x + 10)

= - \frac{1}{2 ( x + 10 ) ^{\frac{3}{2}}} \frac{d}{d x} (x + 10)

\frac{d}{d x} (x + 10) = 1

= \frac{1}{2} (- \frac{1}{2 ( x + 10 ) ^{\frac{3}{2}}} \cdot 1)

Simplify

\frac{1}{2} (- \frac{1}{2 ( x + 10 ) ^{\frac{3}{2}}} \cdot 1) : - \frac{1}{4 ( x + 10 ) ^{\frac{3}{2}}}

= - \frac{1}{4 ( x + 10 ) ^{\frac{3}{2}}}

y^{^{'}} = 2 x e^{y}

\frac{\partial}{\partial x} (e^{x y} cos (b x + c))

\frac{d y}{d x} = 2 + y - 2 x + 4

\frac{d y}{d x}, 2 x y = 6

(8.3) (3.5)

What is the derivative of 1/(2sqrt(x+10)) ?
The derivative of 1/(2sqrt(x+10)) is -1/(4(x+10)^{3/2)}
What is the first derivative of 1/(2sqrt(x+10)) ?
The first derivative of 1/(2sqrt(x+10)) is -1/(4(x+10)^{3/2)}