What is the derivative of 1/(sqrt(64+5t^2)) ?

The derivative of 1/(sqrt(64+5t^2)) is -(5t)/((64+5t^2)^{3/2)}

What is the first derivative of 1/(sqrt(64+5t^2)) ?

The first derivative of 1/(sqrt(64+5t^2)) is -(5t)/((64+5t^2)^{3/2)}

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derivative of

\frac{1}{64 + 5 t ^{2}}

- \frac{5 t}{( 64 + 5 t ^{2} ) ^{\frac{3}{2}}}

Solution steps

\frac{d}{d t} (\frac{1}{64 + 5 t ^{2}})

Apply exponent rule:

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

= \frac{d}{d t} ((64 + 5 t^{2})^{- \frac{1}{2}})

Apply the chain rule:

- \frac{1}{2 ( 64 + 5 t ^{2} ) ^{\frac{3}{2}}} \frac{d}{d t} (64 + 5 t^{2})

= - \frac{1}{2 ( 64 + 5 t ^{2} ) ^{\frac{3}{2}}} \frac{d}{d t} (64 + 5 t^{2})

\frac{d}{d t} (64 + 5 t^{2}) = 10 t

= - \frac{1}{2 ( 64 + 5 t ^{2} ) ^{\frac{3}{2}}} \cdot 10 t

Simplify

- \frac{1}{2 ( 64 + 5 t ^{2} ) ^{\frac{3}{2}}} \cdot 10 t : - \frac{5 t}{( 64 + 5 t ^{2} ) ^{\frac{3}{2}}}

= - \frac{5 t}{( 64 + 5 t ^{2} ) ^{\frac{3}{2}}}

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\int_{0}^{t} e^{x} \cdot sin (π \cdot x) d x

6 e^{x} cos (x)

x \to 6 lim (x^{2} - 36)

What is the derivative of 1/(sqrt(64+5t^2)) ?
The derivative of 1/(sqrt(64+5t^2)) is -(5t)/((64+5t^2)^{3/2)}
What is the first derivative of 1/(sqrt(64+5t^2)) ?
The first derivative of 1/(sqrt(64+5t^2)) is -(5t)/((64+5t^2)^{3/2)}