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Popular >

derivative of 5x^3ln(x)

Solution

\frac{d}{d x} (5 x^{3} ln (x))

Solution

5 (3 x^{2} ln (x) + x^{2})

Solution steps

\frac{d}{d x} (5 x^{3} ln (x))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 5 \frac{d}{d x} (x^{3} ln (x))

Apply the Product Rule:

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

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

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

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

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

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

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

= 5 (3 x^{2} ln (x) + x^{2})

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inverse oflaplace s^2+7s+12 inverse laplace

s^{2} + 7 s + 12

(dy)/(dx)=((5y^4-2xy))/(x^2)

\frac{d y}{d x} = \frac{( 5 y ^{4} - 2 x y )}{x ^{2}}

derivative of 12x^3-36x^2

\frac{d}{d x} (12 x^{3} - 36 x^{2})

Frequently Asked Questions (FAQ)

What is the derivative of 5x^3ln(x) ?
The derivative of 5x^3ln(x) is 5(3x^2ln(x)+x^2)
What is the first derivative of 5x^3ln(x) ?
The first derivative of 5x^3ln(x) is 5(3x^2ln(x)+x^2)