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Popular >

derivative of sqrt(x^2+3x)-x

Solution

\frac{d}{d x} (x^{2} + 3 x - x)

Solution

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

Solution steps

\frac{d}{d x} (x^{2} + 3 x - x)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (x^{2} + 3 x) - \frac{d x}{d x}

\frac{d}{d x} (x^{2} + 3 x) = \frac{2 x + 3}{2 x ^{2} + 3 x}

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

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

Graph

Popular Examples

y^{''}+6y=0,y^'(1)=5

y^{^{''}} + 6 y = 0, y^{^{'}} (1) = 5

(dy)/(dx)=((x^2+1))/(y^2+1),y(0)=1

\frac{d y}{d x} = \frac{( x ^{2} + 1 )}{y ^{2} + 1}, y (0) = 1

derivative of arccos(1-2x^2)

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

limit as x approaches 3 of (\sqrt[3]{x^2-1}-2)/(x-3)

x \to 3 lim (\frac{3 x ^{2} - 1 - 2}{x - 3})

area y=6-6x,y=0,x=0 area

y = 6 - 6 x, y = 0, x = 0

Frequently Asked Questions (FAQ)

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