What is the derivative of (1-x/2)^{e^{x^2}} ?

The derivative of (1-x/2)^{e^{x^2}} is (2e^{x^2}xln(1-x/2)-(e^{x^2})/(2-x))(1-x/2)^{e^{x^2}}

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

The first derivative of (1-x/2)^{e^{x^2}} is (2e^{x^2}xln(1-x/2)-(e^{x^2})/(2-x))(1-x/2)^{e^{x^2}}

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derivative of

(1 - \frac{x}{2})^{e^{x^{2}}}

(2 e^{x^{2}} x ln (1 - \frac{x}{2}) - \frac{e ^{x^{2}}}{2 - x}) (1 - \frac{x}{2})^{e^{x^{2}}}

Solution steps

\frac{d}{d x} ((1 - \frac{x}{2})^{e^{x^{2}}})

Apply exponent rule:

a^{b} = e^{b l n (a)}

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

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

Apply the chain rule:

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

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

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

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

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

= (2 e^{x^{2}} x ln (1 - \frac{x}{2}) - \frac{e ^{x^{2}}}{2 - x}) (1 - \frac{x}{2})^{e^{x^{2}}}

n = 1 \sum \infty \frac{4}{n ^{3}}

y^{^{''}} + 36 y = - 2 tan (6 x)

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

f^{^{'}} (x) = 3 cos (x) + 4 (- sin (x))

x \to 0 + lim (\frac{2}{ln ( x )})

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