What is the derivative of 3^{sqrt(x^2-1)} ?

The derivative of 3^{sqrt(x^2-1)} is (ln(3)*3^{sqrt(x^2-1)}x)/(sqrt(x^2-1))

What is the first derivative of 3^{sqrt(x^2-1)} ?

The first derivative of 3^{sqrt(x^2-1)} is (ln(3)*3^{sqrt(x^2-1)}x)/(sqrt(x^2-1))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d x} (3^{x^{2} - 1})

\frac{ln ( 3 ) \cdot 3 ^{x^{2} - 1} x}{x ^{2} - 1}

Solution steps

\frac{d}{d x} (3^{x^{2} - 1})

Apply exponent rule:

a^{b} = e^{b l n (a)}

3^{x^{2} - 1} = e^{x^{2} - 1 l n (3)}

= \frac{d}{d x} (e^{x^{2} - 1 l n (3)})

Apply the chain rule:

e^{x^{2} - 1 l n (3)} \frac{d}{d x} (x^{2} - 1 ln (3))

= e^{x^{2} - 1 l n (3)} \frac{d}{d x} (x^{2} - 1 ln (3))

\frac{d}{d x} (x^{2} - 1 ln (3)) = \frac{ln ( 3 ) x}{x ^{2} - 1}

= e^{x^{2} - 1 l n (3)} \frac{ln ( 3 ) x}{x ^{2} - 1}

Simplify

e^{x^{2} - 1 l n (3)} \frac{ln ( 3 ) x}{x ^{2} - 1} : \frac{ln ( 3 ) \cdot 3 ^{x^{2} - 1} x}{x ^{2} - 1}

= \frac{ln ( 3 ) \cdot 3 ^{x^{2} - 1} x}{x ^{2} - 1}

\frac{d}{d x} (a t^{5} - 5 b t^{3})

x \to - 2 - lim (2 x + 4 - 2)

\int cos (2 x) tan (2 x) d x

z \to 1 lim (\frac{z + 2}{z ^{4} - 1})

f (x) = (x - 2)^{2} (x + 3)^{3}

What is the derivative of 3^{sqrt(x^2-1)} ?
The derivative of 3^{sqrt(x^2-1)} is (ln(3)*3^{sqrt(x^2-1)}x)/(sqrt(x^2-1))
What is the first derivative of 3^{sqrt(x^2-1)} ?
The first derivative of 3^{sqrt(x^2-1)} is (ln(3)*3^{sqrt(x^2-1)}x)/(sqrt(x^2-1))