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Popular >

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

Solution

derivative of

f (x) = 5 x^{5} ln (x)

Solution

5 (5 x^{4} ln (x) + x^{4})

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

f = x^{5}, g = ln (x)

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

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

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

= 5 (5 x^{4} ln (x) + \frac{1}{x} x^{5})

\frac{1}{x} x^{5} = x^{4}

= 5 (5 x^{4} ln (x) + x^{4})

Popular Examples

(dy)/(dx)= y/x+5x+4

\frac{d y}{d x} = \frac{y}{x} + 5 x + 4

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

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

(\partial)/(\partial x)(14xe^y)

\frac{\partial}{\partial x} (14 x e^{y})

x^{2} y^{^{'}} = y^{2} + x^{2}

derivative of (x+2e^{-x})

\frac{d}{d x} ((x + 2) e^{- x})

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=5x^5ln(x) ?
The derivative of f(x)=5x^5ln(x) is 5(5x^4ln(x)+x^4)
What is the first derivative of f(x)=5x^5ln(x) ?
The first derivative of f(x)=5x^5ln(x) is 5(5x^4ln(x)+x^4)