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

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

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

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

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derivative of

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

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

\frac{d}{d t} (1 + 4 t^{2}) = 8 t

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

Simplify

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

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

s l o p e \frac{5}{x}

\int_{0}^{1} 3^{- x} d x

\int_{b}^{2 b} x^{6} d x

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

x \to 0 lim (1 - e^{x})

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