en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of (e^x/(7x^2+5))

Solution

\frac{d}{d x} (\frac{e ^{x}}{7 x ^{2} + 5})

Solution

\frac{e ^{x} ( 7 x ^{2} + 5 ) - 14 x e ^{x}}{( 7 x ^{2} + 5 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{e ^{x}}{7 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 ^{x} ) ( 7 x ^{2} + 5 ) - \frac{d}{d x} ( 7 x ^{2} + 5 ) e ^{x}}{( 7 x ^{2} + 5 ) ^{2}}

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

\frac{d}{d x} (7 x^{2} + 5) = 14 x

= \frac{e ^{x} ( 7 x ^{2} + 5 ) - 14 x e ^{x}}{( 7 x ^{2} + 5 ) ^{2}}

Popular Examples

y^{''}+5y^'+4y=8x^2

y^{^{''}} + 5 y^{^{'}} + 4 y = 8 x^{2}

xy^{''}+3y^'=1984(x^{19})^{82}

x y^{^{''}} + 3 y^{^{'}} = 1984 (x^{19})^{82}

integral of (10800x)/(9x^2+675)

\int \frac{10800 x}{9 x ^{2} + 675} d x

derivative of sin(x^2+e^x)

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

derivative of f(x)=(5x^4-3x^3)/(x^5)derivative of

f (x) = \frac{5 x ^{4} - 3 x ^{3}}{x ^{5}}

Frequently Asked Questions (FAQ)

What is the derivative of (e^x/(7x^2+5)) ?
The derivative of (e^x/(7x^2+5)) is (e^x(7x^2+5)-14xe^x)/((7x^2+5)^2)
What is the first derivative of (e^x/(7x^2+5)) ?
The first derivative of (e^x/(7x^2+5)) is (e^x(7x^2+5)-14xe^x)/((7x^2+5)^2)