en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of 7^{x^4+2}

Solution

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

Solution

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

Solution steps

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

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

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

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

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

Popular Examples

derivative of ln(ln(9x))

\frac{d}{d x} (ln (ln (9 x)))

integral from 0 to 9 of 2piy(3-y/3)

\int_{0}^{9} 2 π y (3 - \frac{y}{3}) d y

derivative of-(5e^{5/x}/(x^2))

\frac{d}{d x} (- \frac{5 e ^{\frac{5}{x}}}{x ^{2}})

(\partial)/(\partial x)(30-(x^2+y^2))

\frac{\partial}{\partial x} (30 - (x^{2} + y^{2}))

integral of sin^5(11x)

\int sin^{5} (11 x) d x

Frequently Asked Questions (FAQ)

What is the derivative of 7^{x^4+2} ?
The derivative of 7^{x^4+2} is 4ln(7)*7^{x^4+2}x^3
What is the first derivative of 7^{x^4+2} ?
The first derivative of 7^{x^4+2} is 4ln(7)*7^{x^4+2}x^3