What is the derivative of a^{{f}(x(x^2)}) ?

The derivative of a^{{f}(x(x^2)}) is a^{x^2{f}(x)}ln(a)(x^2 derivative of {f}(x)+2x{f}(x))

What is the first derivative of a^{{f}(x(x^2)}) ?

The first derivative of a^{{f}(x(x^2)}) is a^{x^2{f}(x)}ln(a)(x^2 derivative of {f}(x)+2x{f}(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} (a^{f (x) (x^{2})})

a^{x^{2} f (x)} ln (a) (x^{2} \frac{d}{d x} (f (x)) + 2 x f (x))

Solution steps

\frac{d}{d x} (a^{f (x) (x^{2})})

Apply exponent rule:

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

a^{f (x) x^{2}} = e^{f (x) x^{2} l n (a)}

= \frac{d}{d x} (e^{f (x) x^{2} l n (a)})

Apply the chain rule:

e^{f (x) x^{2} l n (a)} \frac{d}{d x} (f (x) x^{2} ln (a))

= e^{f (x) x^{2} l n (a)} \frac{d}{d x} (f (x) x^{2} ln (a))

\frac{d}{d x} (f (x) x^{2} ln (a)) = ln (a) (\frac{d}{d x} (f (x)) x^{2} + 2 x f (x))

= e^{f (x) x^{2} l n (a)} ln (a) (\frac{d}{d x} (f (x)) x^{2} + 2 x f (x))

e^{f (x) x^{2} l n (a)} = a^{x^{2} f (x)}

= a^{x^{2} f (x)} ln (a) (x^{2} \frac{d}{d x} (f (x)) + 2 x f (x))

\frac{\partial}{\partial x} (e^{y} (y^{2} - x^{2}))

(tan (x))^{^{'}}

y = - 2 x^{3}, (- 2, 16)

x \to 0 lim ((1 - 2 x)^{\frac{4}{x}})

\int \frac{2 y}{3} d y

What is the derivative of a^{{f}(x(x^2)}) ?
The derivative of a^{{f}(x(x^2)}) is a^{x^2{f}(x)}ln(a)(x^2 derivative of {f}(x)+2x{f}(x))
What is the first derivative of a^{{f}(x(x^2)}) ?
The first derivative of a^{{f}(x(x^2)}) is a^{x^2{f}(x)}ln(a)(x^2 derivative of {f}(x)+2x{f}(x))