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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\frac{d}{d x} ((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}}}

x \frac{d y}{d x} + (3 x + 1) y = e^{3 x}

(6 y + 2 t - 7) d t + (8 y + 6 t - 1) d y = 0

\int \frac{x}{3 - 2 x - x ^{2}} d x

y^{^{'}} = t y^{2}

\int_{2}^{\frac{1}{x}} arctan (t) d t

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}}