en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

derivative of (e^{6x}/(x^2+5))

Solution

\frac{d}{d x} (\frac{e ^{6 x}}{x ^{2} + 5})

Solution

\frac{e ^{6 x} \cdot 6 ( x ^{2} + 5 ) - 2 x e ^{6 x}}{( x ^{2} + 5 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{e ^{6 x}}{x ^{2} + 5})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( e ^{6 x} ) ( x ^{2} + 5 ) - \frac{d}{d x} ( x ^{2} + 5 ) e ^{6 x}}{( x ^{2} + 5 ) ^{2}}

\frac{d}{d x} (e^{6 x}) = e^{6 x} \cdot 6

\frac{d}{d x} (x^{2} + 5) = 2 x

= \frac{e ^{6 x} \cdot 6 ( x ^{2} + 5 ) - 2 x e ^{6 x}}{( x ^{2} + 5 ) ^{2}}

Graph

Popular Examples

derivative of f(t)=(2t-1)^7+14t(2t-1)^6 derivative of

f (t) = (2 t - 1)^{7} + 14 t (2 t - 1)^{6}

y^'=(x+y-4)^2,y(0)=0

y^{^{'}} = (x + y - 4)^{2}, y (0) = 0

inverse oflaplace (10)/((2s+3))inverse laplace

\frac{10}{( 2 s + 3 )}

simplify (x^4)/4+1/(8x^2)simplify

\frac{x ^{4}}{4} + \frac{1}{8 x ^{2}}

derivative of (x^2-x+1^{-7})

\frac{d}{d x} ((x^{2} - x + 1)^{- 7})

Frequently Asked Questions (FAQ)

What is the derivative of (e^{6x}/(x^2+5)) ?
The derivative of (e^{6x}/(x^2+5)) is (e^{6x}*6(x^2+5)-2xe^{6x})/((x^2+5)^2)
What is the first derivative of (e^{6x}/(x^2+5)) ?
The first derivative of (e^{6x}/(x^2+5)) is (e^{6x}*6(x^2+5)-2xe^{6x})/((x^2+5)^2)