What is the derivative of 10^{(x^2-1}) ?

The derivative of 10^{(x^2-1}) is ln(10)*2^{x^2}*5^{x^2-1}x

What is the first derivative of 10^{(x^2-1}) ?

The first derivative of 10^{(x^2-1}) is ln(10)*2^{x^2}*5^{x^2-1}x

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d x} (1 0^{(x^{2} - 1)})

ln (10) \cdot 2^{x^{2}} \cdot 5^{x^{2} - 1} x

Solution steps

\frac{d}{d x} (1 0^{(x^{2} - 1)})

Apply exponent rule:

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

1 0^{x^{2} - 1} = e^{(x^{2} - 1) l n (10)}

= \frac{d}{d x} (e^{(x^{2} - 1) l n (10)})

Apply the chain rule:

e^{(x^{2} - 1) l n (10)} \frac{d}{d x} ((x^{2} - 1) ln (10))

= e^{(x^{2} - 1) l n (10)} \frac{d}{d x} ((x^{2} - 1) ln (10))

\frac{d}{d x} ((x^{2} - 1) ln (10)) = 2 ln (10) x

= e^{(x^{2} - 1) l n (10)} \cdot 2 ln (10) x

Simplify

e^{(x^{2} - 1) l n (10)} \cdot 2 ln (10) x : ln (10) \cdot 2^{x^{2}} \cdot 5^{x^{2} - 1} x

= ln (10) \cdot 2^{x^{2}} \cdot 5^{x^{2} - 1} x

\int \frac{15 e ^{5 x}}{e ^{5 x} + 2} d x

f (x) = - 4 x^{2} + 7 x - 14, at x = - 2

\frac{\partial}{\partial x} (x^{c o s (x)})

e^{18 x}

x \to \infty lim (x^{(\frac{1}{x ^{2} - 1})})

What is the derivative of 10^{(x^2-1}) ?
The derivative of 10^{(x^2-1}) is ln(10)*2^{x^2}*5^{x^2-1}x
What is the first derivative of 10^{(x^2-1}) ?
The first derivative of 10^{(x^2-1}) is ln(10)*2^{x^2}*5^{x^2-1}x