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Popular >

derivative of x^{12}ln(x)

Solution

\frac{d}{d x} (x^{12} ln (x))

Solution

12 x^{11} ln (x) + x^{11}

Solution steps

\frac{d}{d x} (x^{12} ln (x))

Apply the Product Rule:

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

f = x^{12}, g = ln (x)

= \frac{d}{d x} (x^{12}) ln (x) + \frac{d}{d x} (ln (x)) x^{12}

\frac{d}{d x} (x^{12}) = 12 x^{11}

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

= 12 x^{11} ln (x) + \frac{1}{x} x^{12}

\frac{1}{x} x^{12} = x^{11}

= 12 x^{11} ln (x) + x^{11}

Popular Examples

integral of (16)/(x(x^2+4)^2)

\int \frac{16}{x ( x ^{2} + 4 ) ^{2}} d x

derivative of (xsin(2x)^{3/2})

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

integral of ((x+16))/((x^2+2x-8))

\int \frac{( x + 16 )}{( x ^{2} + 2 x - 8 )} d x

(\partial)/(\partial α)({K}(α)(α)^αL^{1-α})

\frac{\partial}{\partial α} (K (α) (α)^{α} L^{1 - α})

tangent of y=11x^2,(-2,44)tangent of

y = 11 x^{2}, (- 2, 44)

Frequently Asked Questions (FAQ)

What is the derivative of x^{12}ln(x) ?
The derivative of x^{12}ln(x) is 12x^{11}ln(x)+x^{11}
What is the first derivative of x^{12}ln(x) ?
The first derivative of x^{12}ln(x) is 12x^{11}ln(x)+x^{11}