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Popular >

derivative of sqrt(x^2+6x-1)

Solution

derivative of

x^{2} + 6 x - 1

Solution

\frac{x + 3}{x ^{2} + 6 x - 1}

Solution steps

\frac{d}{d x} (x^{2} + 6 x - 1)

Apply the chain rule:

\frac{1}{2 x ^{2} + 6 x - 1} \frac{d}{d x} (x^{2} + 6 x - 1)

= \frac{1}{2 x ^{2} + 6 x - 1} \frac{d}{d x} (x^{2} + 6 x - 1)

\frac{d}{d x} (x^{2} + 6 x - 1) = 2 x + 6

= \frac{1}{2 x ^{2} + 6 x - 1} (2 x + 6)

Simplify

\frac{1}{2 x ^{2} + 6 x - 1} (2 x + 6) : \frac{x + 3}{x ^{2} + 6 x - 1}

= \frac{x + 3}{x ^{2} + 6 x - 1}

Popular Examples

integral of-2x^4tan(x^5)

\int - 2 x^{4} tan (x^{5}) d x

(\partial)/(\partial y)(4x^3y^2+2)

\frac{\partial}{\partial y} (4 x^{3} y^{2} + 2)

x^2y^{''}+xy^'-9y=x^3+1

x^{2} y^{^{''}} + x y^{^{'}} - 9 y = x^{3} + 1

sum from n=0 to infinity of (1+2/n)^{3n}

n = 0 \sum \infty (1 + \frac{2}{n})^{3 n}

derivative of x^a(1-x^b)

\frac{d}{d x} (x^{a} (1 - x)^{b})

Frequently Asked Questions (FAQ)

What is the derivative of sqrt(x^2+6x-1) ?
The derivative of sqrt(x^2+6x-1) is (x+3)/(sqrt(x^2+6x-1))
What is the first derivative of sqrt(x^2+6x-1) ?
The first derivative of sqrt(x^2+6x-1) is (x+3)/(sqrt(x^2+6x-1))