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Popular >

derivative of x+3sqrt(3x^2-2x+5)

Solution

derivative of

x + 3 3 x^{2} - 2 x + 5

Solution

1 + \frac{3 ( 3 x - 1 )}{3 x ^{2} - 2 x + 5}

Solution steps

\frac{d}{d x} (x + 3 3 x^{2} - 2 x + 5)

Apply the Sum/Difference Rule:

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

= \frac{d x}{d x} + \frac{d}{d x} (3 3 x^{2} - 2 x + 5)

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

\frac{d}{d x} (3 3 x^{2} - 2 x + 5) = \frac{3 ( 3 x - 1 )}{3 x ^{2} - 2 x + 5}

= 1 + \frac{3 ( 3 x - 1 )}{3 x ^{2} - 2 x + 5}

Popular Examples

-y^2-ye^t+(y+e^t)((dy)/(dt))=0

- y^{2} - y e^{t} + (y + e^{t}) (\frac{d y}{d t}) = 0

integral of 1/((6x^2+9)^4)x

\int \frac{1}{( 6 x ^{2} + 9 ) ^{4}} x d x

limit as x approaches infinity of 1+6/x

x \to \infty lim (1 + \frac{6}{x})

integral from 0 to pi/6 of sin(2x)

\int_{0}^{\frac{π}{6}} sin (2 x) d x

integral of 3x^2sin(3x)

\int 3 x^{2} sin (3 x) d x

Frequently Asked Questions (FAQ)

What is the derivative of x+3sqrt(3x^2-2x+5) ?
The derivative of x+3sqrt(3x^2-2x+5) is 1+(3(3x-1))/(sqrt(3x^2-2x+5))
What is the first derivative of x+3sqrt(3x^2-2x+5) ?
The first derivative of x+3sqrt(3x^2-2x+5) is 1+(3(3x-1))/(sqrt(3x^2-2x+5))