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Popular >

derivative of 2x^5ln(x)

Solution

derivative of

2 x^{5} ln (x)

Solution

2 (5 x^{4} ln (x) + x^{4})

Solution steps

\frac{d}{d x} (2 x^{5} ln (x))

Take the constant out:

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

= 2 \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)

= 2 (\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}

= 2 (5 x^{4} ln (x) + \frac{1}{x} x^{5})

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

= 2 (5 x^{4} ln (x) + x^{4})

Popular Examples

derivative of f(x)=(3x+1)/(5+x)derivative of

f (x) = \frac{3 x + 1}{5 + x}

integral of 7/(x(x^2+4)^2)

\int \frac{7}{x ( x ^{2} + 4 ) ^{2}} d x

derivative of e^{x^2-4}

\frac{d}{d x} (e^{x^{2} - 4})

derivative of 14(2x+5^6)

\frac{d}{d x} (14 (2 x + 5)^{6})

limit as x approaches 2-of (4x)/(x-2)

x \to 2 - lim (\frac{4 x}{x - 2})

Frequently Asked Questions (FAQ)

What is the derivative of 2x^5ln(x) ?
The derivative of 2x^5ln(x) is 2(5x^4ln(x)+x^4)
What is the first derivative of 2x^5ln(x) ?
The first derivative of 2x^5ln(x) is 2(5x^4ln(x)+x^4)