What is (\partial)/(\partial x)(7^{x^4+2x}) ?

The answer to (\partial)/(\partial x)(7^{x^4+2x}) is ln(7)*7^{x^4+2x}(4x^3+2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(\partial)/(\partial x)(7^{x^4+2x})

\frac{\partial}{\partial x} (7^{x^{4} + 2 x})

ln (7) \cdot 7^{x^{4} + 2 x} (4 x^{3} + 2)

Solution steps

\frac{\partial}{\partial x} (7^{x^{4} + 2 x})

Apply exponent rule:

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

7^{x^{4} + 2 x} = e^{(x^{4} + 2 x) l n (7)}

= \frac{\partial}{\partial x} (e^{(x^{4} + 2 x) l n (7)})

Apply the chain rule:

e^{(x^{4} + 2 x) l n (7)} \frac{\partial}{\partial x} ((x^{4} + 2 x) ln (7))

= e^{(x^{4} + 2 x) l n (7)} \frac{\partial}{\partial x} ((x^{4} + 2 x) ln (7))

\frac{\partial}{\partial x} ((x^{4} + 2 x) ln (7)) = ln (7) (4 x^{3} + 2)

= e^{(x^{4} + 2 x) l n (7)} ln (7) (4 x^{3} + 2)

e^{(x^{4} + 2 x) l n (7)} = 7^{x^{4} + 2 x}

= ln (7) \cdot 7^{x^{4} + 2 x} (4 x^{3} + 2)

What is (\partial)/(\partial x)(7^{x^4+2x}) ?
The answer to (\partial)/(\partial x)(7^{x^4+2x}) is ln(7)*7^{x^4+2x}(4x^3+2)