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Popular >

derivative of (x+3ln(x^2))

Solution

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

Solution

2 ln (x) + \frac{2 ( x + 3 )}{x}

Solution steps

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

Apply the Product Rule:

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

f = x + 3, g = ln (x^{2})

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

\frac{d}{d x} (x + 3) = 1

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

= 1 \cdot ln (x^{2}) + \frac{2}{x} (x + 3)

Simplify

1 \cdot ln (x^{2}) + \frac{2}{x} (x + 3) : 2 ln (x) + \frac{2 ( x + 3 )}{x}

= 2 ln (x) + \frac{2 ( x + 3 )}{x}

Graph

Popular Examples

y+2y^7=(y^3+6x)y^'

y + 2 y^{7} = (y^{3} + 6 x) y^{^{'}}

derivative of x^2-x derivative of

x^{2} - x

limit as x approaches 0+of x/(x+1)

x \to 0 + lim (\frac{x}{x + 1})

(\partial)/(\partial x)((x+2y+3z)^{3/2})

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

derivative of y=6e^{3x}derivative of

y = 6 e^{3 x}

Frequently Asked Questions (FAQ)

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