What is the derivative of sqrt(t^2+a^2) ?

The derivative of sqrt(t^2+a^2) is t/(sqrt(t^2+a^2))

What is the first derivative of sqrt(t^2+a^2) ?

The first derivative of sqrt(t^2+a^2) is t/(sqrt(t^2+a^2))

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derivative of

t^{2} + a^{2}

\frac{t}{t ^{2} + a ^{2}}

Solution steps

\frac{d}{d t} (t^{2} + a^{2})

Treat

a

as a constant

Apply the chain rule:

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

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

\frac{d}{d t} (t^{2} + a^{2}) = 2 t

= \frac{1}{2 t ^{2} + a ^{2}} \cdot 2 t

Simplify

\frac{1}{2 t ^{2} + a ^{2}} \cdot 2 t : \frac{t}{t ^{2} + a ^{2}}

= \frac{t}{t ^{2} + a ^{2}}

\frac{d}{d x} (x^{4} e^{10 x})

\frac{d}{d x} (\frac{8}{5} x^{- \frac{2}{4}})

f (x) = x^{3} + 2 x, at x = 3

x \to 1 lim (7)

x^{4}

What is the derivative of sqrt(t^2+a^2) ?
The derivative of sqrt(t^2+a^2) is t/(sqrt(t^2+a^2))
What is the first derivative of sqrt(t^2+a^2) ?
The first derivative of sqrt(t^2+a^2) is t/(sqrt(t^2+a^2))