en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of f(x)=sqrt(5x^2+5x+7)

Solution

derivative of

f (x) = 5 x^{2} + 5 x + 7

Solution

\frac{10 x + 5}{2 5 x ^{2} + 5 x + 7}

Solution steps

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

Apply the chain rule:

\frac{1}{2 5 x ^{2} + 5 x + 7} \frac{d}{d x} (5 x^{2} + 5 x + 7)

= \frac{1}{2 5 x ^{2} + 5 x + 7} \frac{d}{d x} (5 x^{2} + 5 x + 7)

\frac{d}{d x} (5 x^{2} + 5 x + 7) = 10 x + 5

= \frac{1}{2 5 x ^{2} + 5 x + 7} (10 x + 5)

Simplify

\frac{1}{2 5 x ^{2} + 5 x + 7} (10 x + 5) : \frac{10 x + 5}{2 5 x ^{2} + 5 x + 7}

= \frac{10 x + 5}{2 5 x ^{2} + 5 x + 7}

Popular Examples

(\partial)/(\partial x)(arctan(y/((x-1))))

\frac{\partial}{\partial x} (arctan (\frac{y}{( x - 1 )}))

(\partial)/(\partial x)(sqrt(62-2x^2-2y^2))

\frac{\partial}{\partial x} (62 - 2 x^{2} - 2 y^{2})

derivative of ln(1/(1+x))

\frac{d}{d x} (ln (\frac{1}{1 + x}))

f (x) = arcsec (x)

y^{^{'}} + 7 x e^{y} = 0

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=sqrt(5x^2+5x+7) ?
The derivative of f(x)=sqrt(5x^2+5x+7) is (10x+5)/(2sqrt(5x^2+5x+7))
What is the first derivative of f(x)=sqrt(5x^2+5x+7) ?
The first derivative of f(x)=sqrt(5x^2+5x+7) is (10x+5)/(2sqrt(5x^2+5x+7))