What is the derivative of (-0.4/(sqrt(5+5x))) ?

The derivative of (-0.4/(sqrt(5+5x))) is 1/((5+5x)^{3/2)}

What is the first derivative of (-0.4/(sqrt(5+5x))) ?

The first derivative of (-0.4/(sqrt(5+5x))) is 1/((5+5x)^{3/2)}

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\frac{d}{d x} (\frac{- 0.4}{5 + 5 x})

\frac{1}{( 5 + 5 x ) ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (\frac{- 0.4}{5 + 5 x})

Simplify

\frac{- 0.4}{5 + 5 x} : - \frac{0.4}{5 + 5 x}

= \frac{d}{d x} (- \frac{0.4}{5 + 5 x})

Take the constant out:

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

= - 0.4 \frac{d}{d x} (\frac{1}{5 + 5 x})

Apply exponent rule:

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

= - 0.4 \frac{d}{d x} ((5 + 5 x)^{- \frac{1}{2}})

Apply the chain rule:

- \frac{1}{2 ( 5 + 5 x ) ^{\frac{3}{2}}} \frac{d}{d x} (5 + 5 x)

= - \frac{1}{2 ( 5 + 5 x ) ^{\frac{3}{2}}} \frac{d}{d x} (5 + 5 x)

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

= - 0.4 (- \frac{1}{2 ( 5 + 5 x ) ^{\frac{3}{2}}} \cdot 5)

Simplify

- 0.4 (- \frac{1}{2 ( 5 + 5 x ) ^{\frac{3}{2}}} \cdot 5) : \frac{1}{( 5 + 5 x ) ^{\frac{3}{2}}}

= \frac{1}{( 5 + 5 x ) ^{\frac{3}{2}}}

\frac{d y}{d x} + 0.1 y = 10

\int_{1}^{2} \frac{3 ^{l n (x)}}{x} d x

\int 2^{3 x} d x

x \to 0 lim ((1 + 8 x)^{\frac{5}{x}})

\frac{d ^{2}}{d r ( θ ) d θ} (r (θ) sin (θ))

What is the derivative of (-0.4/(sqrt(5+5x))) ?
The derivative of (-0.4/(sqrt(5+5x))) is 1/((5+5x)^{3/2)}
What is the first derivative of (-0.4/(sqrt(5+5x))) ?
The first derivative of (-0.4/(sqrt(5+5x))) is 1/((5+5x)^{3/2)}