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Popular >

derivative of sqrt(x)+x^2+ln(x)

Solution

derivative of

x + x^{2} + ln (x)

Solution

\frac{x + 2 + 4 x ^{2}}{2 x}

Solution steps

\frac{d}{d x} (x + x^{2} + ln (x))

Apply the Sum/Difference Rule:

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

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

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

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

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

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

Simplify

\frac{1}{2 x} + 2 x + \frac{1}{x} : \frac{x + 2 + 4 x ^{2}}{2 x}

= \frac{x + 2 + 4 x ^{2}}{2 x}

Popular Examples

limit as x approaches+2pi of f(x)

x \to + 2 π lim (f (x))

derivative of ln(x^3+3x)derivative of

ln (x^{3} + 3 x)

\frac{d x}{d y} = 5 x + y

(dy)/(dx)=y^2,y(1)=1

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

integral of (2x+1)/(x(x+1)^2)

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

Frequently Asked Questions (FAQ)

What is the derivative of sqrt(x)+x^2+ln(x) ?
The derivative of sqrt(x)+x^2+ln(x) is (sqrt(x)+2+4x^2)/(2x)
What is the first derivative of sqrt(x)+x^2+ln(x) ?
The first derivative of sqrt(x)+x^2+ln(x) is (sqrt(x)+2+4x^2)/(2x)