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Popular >

derivative of e^xln(x^2)

Solution

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

Solution

2 e^{x} ln (x) + \frac{2 e ^{x}}{x}

Solution steps

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

Apply the Product Rule:

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

f = e^{x}, g = ln (x^{2})

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

\frac{d}{d x} (e^{x}) = e^{x}

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

= e^{x} ln (x^{2}) + \frac{2}{x} e^{x}

Simplify

e^{x} ln (x^{2}) + \frac{2}{x} e^{x} : 2 e^{x} ln (x) + \frac{2 e ^{x}}{x}

= 2 e^{x} ln (x) + \frac{2 e ^{x}}{x}

Popular Examples

(dy)/(dx)=(xy)/(x^2+1)

\frac{d y}{d x} = \frac{x y}{x ^{2} + 1}

derivative of f(x)=-3x^2+24x-36 derivative of

f (x) = - 3 x^{2} + 24 x - 36

y^'=(2x)/(1+2y)

y^{^{'}} = \frac{2 x}{1 + 2 y}

tangent of f(x)=6sin(x),(pi/6 ,3)tangent of

f (x) = 6 sin (x), (\frac{π}{6}, 3)

(\partial)/(\partial u(v))((e^v)/(u(v)+v^8))

\frac{\partial}{\partial u ( v )} (\frac{e ^{v}}{u ( v ) + v ^{8}})

Frequently Asked Questions (FAQ)

What is the derivative of e^xln(x^2) ?
The derivative of e^xln(x^2) is 2e^xln(x)+(2e^x)/x
What is the first derivative of e^xln(x^2) ?
The first derivative of e^xln(x^2) is 2e^xln(x)+(2e^x)/x