en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

(1/4 x^8-3e^x+100ln(x))^'

Solution

(\frac{1}{4} x^{8} - 3 e^{x} + 100 ln (x))^{^{'}}

Solution

2 x^{7} - 3 e^{x} + \frac{100}{x}

Solution steps

(\frac{1}{4} x^{8} - 3 e^{x} + 100 ln (x))^{'}

Simplify

\frac{1}{4} x^{8} - 3 e^{x} + 100 ln (x) : \frac{x ^{8}}{4} - 3 e^{x} + 100 ln (x)

= (\frac{x ^{8}}{4} - 3 e^{x} + 100 ln (x))^{^{'}}

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= (\frac{x ^{8}}{4})^{^{'}} - (3 e^{x})^{^{'}} + (100 ln (x))^{^{'}}

(\frac{x ^{8}}{4})^{'} = 2 x^{7}

(3 e^{x})^{'} = 3 e^{x}

(100 ln (x))^{'} = \frac{100}{x}

= 2 x^{7} - 3 e^{x} + \frac{100}{x}

Graph

Popular Examples

integral of 1/(sqrt(1+2x))

\int \frac{1}{1 + 2 x} d x

cos(x)y^'+sin(x)y=1

cos (x) y^{^{'}} + sin (x) y = 1

integral of (2x+3)/(sqrt(x+2))

\int \frac{2 x + 3}{x + 2} d x

derivative of sin(x^2cos(pix+2))

\frac{d}{d x} (sin (x^{2}) cos (π x + 2))

(\partial)/(\partial y)(4x^3-36x)

\frac{\partial}{\partial y} (4 x^{3} - 36 x)

Frequently Asked Questions (FAQ)

What is the (1/4 x^8-3e^x+100ln(x))^' ?
The (1/4 x^8-3e^x+100ln(x))^' is 2x^7-3e^x+(100)/x
What is the first (1/4 x^8-3e^x+100ln(x))^' ?
The first (1/4 x^8-3e^x+100ln(x))^' is 2x^7-3e^x+(100)/x