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Popular >

derivative of f(x)=5x^3ln(x)

Solution

derivative of

f (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})

Popular Examples

y^{''}+2y^'+5y=0,y(0)=5,y^'(0)=-5

y^{^{''}} + 2 y^{^{'}} + 5 y = 0, y (0) = 5, y^{^{'}} (0) = - 5

x^2y^{''}+3xy^'+4y=0

x^{2} y^{^{''}} + 3 x y^{^{'}} + 4 y = 0

(\partial)/(\partial z)(sin(z^3)cos(xy))

\frac{\partial}{\partial z} (sin (z^{3}) cos (x y))

derivative of f(x)=(-2x)/(x^5-x-1)derivative of

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

integral of yze^{xy}

\int yz e^{x y} d x

Frequently Asked Questions (FAQ)

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