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Popular >

derivative of e^{1+(ln(x))^2}

Solution

derivative of

e^{1 + (l n (x))^{2}}

Solution

\frac{2 e ^{1 + l n^{2} (x)} ln ( x )}{x}

Solution steps

\frac{d}{d x} (e^{1 + (l n (x))^{2}})

Apply the chain rule:

e^{1 + (l n (x))^{2}} \frac{d}{d x} (1 + (ln (x))^{2})

= e^{1 + (l n (x))^{2}} \frac{d}{d x} (1 + (ln (x))^{2})

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

= e^{1 + (l n (x))^{2}} \frac{2 ln ( x )}{x}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{2 e ^{1 + l n^{2} (x)} ln ( x )}{x}

Popular Examples

sqrt(1-y^2)dx-sqrt(1-x^2)dy=0,y(0)= 1/2

1 - y^{2} d x - 1 - x^{2} d y = 0, y (0) = \frac{1}{2}

y^{^{'}} = e^{t - y}

integral of (3x-11)e^x

\int (3 x - 11) e^{x} d x

3y^{''}-7y^'+2y=0,y(0)=-3,y^'(0)=-8

3 y^{^{''}} - 7 y^{^{'}} + 2 y = 0, y (0) = - 3, y^{^{'}} (0) = - 8

integral of sin(x)-8cos(x)

\int sin (x) - 8 cos (x) d x

Frequently Asked Questions (FAQ)

What is the derivative of e^{1+(ln(x))^2} ?
The derivative of e^{1+(ln(x))^2} is (2e^{1+ln^2(x)}ln(x))/x
What is the first derivative of e^{1+(ln(x))^2} ?
The first derivative of e^{1+(ln(x))^2} is (2e^{1+ln^2(x)}ln(x))/x