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Popular >

derivative of y=x^2ln(3x)

Solution

derivative of

y = x^{2} ln (3 x)

Solution

2 x ln (3 x) + x

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

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

= 2 x ln (3 x) + x

Popular Examples

y^'=((1-y)^2)/(x+1),y(0)=5

y^{^{'}} = \frac{( 1 - y ) ^{2}}{x + 1}, y (0) = 5

derivative of ln(ln(sec(x)))

\frac{d}{d x} (ln (ln (sec (x))))

sum from n=1 to infinity of 1-7/(4^n)

n = 1 \sum \infty 1 - \frac{7}{4 ^{n}}

(\partial)/(\partial x)(8-x^2-y^2)

\frac{\partial}{\partial x} (8 - x^{2} - y^{2})

24y^{''}-2y^'-15y=0

24 y^{^{''}} - 2 y^{^{'}} - 15 y = 0

Frequently Asked Questions (FAQ)

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