What is the derivative of sqrt(e^x+19) ?

The derivative of sqrt(e^x+19) is (e^x)/(2sqrt(e^x+19))

What is the first derivative of sqrt(e^x+19) ?

The first derivative of sqrt(e^x+19) is (e^x)/(2sqrt(e^x+19))

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\frac{d}{d x} (e^{x} + 19)

\frac{e ^{x}}{2 e ^{x} + 19}

Solution steps

\frac{d}{d x} (e^{x} + 19)

Apply the chain rule:

\frac{1}{2 e ^{x} + 19} \frac{d}{d x} (e^{x} + 19)

= \frac{1}{2 e ^{x} + 19} \frac{d}{d x} (e^{x} + 19)

\frac{d}{d x} (e^{x} + 19) = e^{x}

= \frac{1}{2 e ^{x} + 19} e^{x}

Simplify

\frac{1}{2 e ^{x} + 19} e^{x} : \frac{e ^{x}}{2 e ^{x} + 19}

= \frac{e ^{x}}{2 e ^{x} + 19}

x \to 2 + lim (2 - x)

\frac{d}{d x} (\frac{1 - 6 x}{2 + x})

(t^{2} + e^{t}) t

\frac{d}{d x} (cos^{2} (x) tan (x))

\frac{d}{d x} (cot (x) d x)

What is the derivative of sqrt(e^x+19) ?
The derivative of sqrt(e^x+19) is (e^x)/(2sqrt(e^x+19))
What is the first derivative of sqrt(e^x+19) ?
The first derivative of sqrt(e^x+19) is (e^x)/(2sqrt(e^x+19))