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}}}

\frac{4 x}{x + 1} (3.3)

y = t (ln (3 t))^{2}

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

\frac{5}{x}

\int 10 x^{\frac{3}{2}} d 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)}