What is the derivative of (-1)/(sqrt(10+4t^2)) ?

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

What is the first derivative of (-1)/(sqrt(10+4t^2)) ?

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

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derivative of

\frac{- 1}{10 + 4 t ^{2}}

\frac{4 t}{( 10 + 4 t ^{2} ) ^{\frac{3}{2}}}

Solution steps

\frac{d}{d t} (\frac{- 1}{10 + 4 t ^{2}})

Simplify

\frac{- 1}{10 + 4 t ^{2}} : - \frac{1}{10 + 4 t ^{2}}

= \frac{d}{d t} (- \frac{1}{10 + 4 t ^{2}})

Take the constant out:

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

= - \frac{d}{d t} (\frac{1}{10 + 4 t ^{2}})

Apply exponent rule:

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

= - \frac{d}{d t} ((10 + 4 t^{2})^{- \frac{1}{2}})

Apply the chain rule:

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

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

\frac{d}{d t} (10 + 4 t^{2}) = 8 t

= - (- \frac{1}{2 ( 10 + 4 t ^{2} ) ^{\frac{3}{2}}} \cdot 8 t)

Simplify

- (- \frac{1}{2 ( 10 + 4 t ^{2} ) ^{\frac{3}{2}}} \cdot 8 t) : \frac{4 t}{( 10 + 4 t ^{2} ) ^{\frac{3}{2}}}

= \frac{4 t}{( 10 + 4 t ^{2} ) ^{\frac{3}{2}}}

\frac{d}{d x} (e^{x + y} sin (x - y))

(x - 2) (x - 3)^{2}

\int - \frac{2 ln ( x )}{x ^{2}} d x

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

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

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