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Popular >

derivative of xsqrt(x+6)

Solution

\frac{d}{d x} (x x + 6)

Solution

\frac{3 x + 12}{2 x + 6}

Solution steps

\frac{d}{d x} (x x + 6)

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = x + 6

= \frac{d x}{d x} x + 6 + \frac{d}{d x} (x + 6) x

\frac{d x}{d x} = 1

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

= 1 \cdot x + 6 + \frac{1}{2 x + 6} x

Simplify

1 \cdot x + 6 + \frac{1}{2 x + 6} x : \frac{3 x + 12}{2 x + 6}

= \frac{3 x + 12}{2 x + 6}

Popular Examples

limit as x approaches infinity of-1/x+1

x \to \infty lim (- \frac{1}{x} + 1)

derivative of f(x)=ln((sqrt(4+x^2))/x)derivative of

f (x) = ln (\frac{4 + x ^{2}}{x})

tangent of f(x)=20sqrt(x),(4,40)tangent of

f (x) = 20 x, (4, 40)

y^{''}+5y^'-2y=0

y^{^{''}} + 5 y^{^{'}} - 2 y = 0

integral of 1/(sqrt(t^2-12t+40))

\int \frac{1}{t ^{2} - 12 t + 40} d t

Frequently Asked Questions (FAQ)

What is the derivative of xsqrt(x+6) ?
The derivative of xsqrt(x+6) is (3x+12)/(2sqrt(x+6))
What is the first derivative of xsqrt(x+6) ?
The first derivative of xsqrt(x+6) is (3x+12)/(2sqrt(x+6))