What is the derivative of e^{{g}(x(x^3)-2x}) ?

The derivative of e^{{g}(x(x^3)-2x}) is e^{{g}(x)x^3-2x}(derivative of {g}(x)x^3+3x^2{g}(x)-2)

What is the first derivative of e^{{g}(x(x^3)-2x}) ?

The first derivative of e^{{g}(x(x^3)-2x}) is e^{{g}(x)x^3-2x}(derivative of {g}(x)x^3+3x^2{g}(x)-2)

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\frac{d}{d x} (e^{g (x) (x^{3}) - 2 x})

e^{g (x) x^{3} - 2 x} (\frac{d}{d x} (g (x)) x^{3} + 3 x^{2} g (x) - 2)

Solution steps

\frac{d}{d x} (e^{g (x) (x^{3}) - 2 x})

Apply the chain rule:

e^{g (x) x^{3} - 2 x} \frac{d}{d x} (g (x) x^{3} - 2 x)

= e^{g (x) x^{3} - 2 x} \frac{d}{d x} (g (x) x^{3} - 2 x)

\frac{d}{d x} (g (x) x^{3} - 2 x) = \frac{d}{d x} (g (x)) x^{3} + 3 x^{2} g (x) - 2

= e^{g (x) x^{3} - 2 x} (\frac{d}{d x} (g (x)) x^{3} + 3 x^{2} g (x) - 2)

\frac{d}{d x} (\frac{x}{x + y})

d er i v a t i v e y = e^{5 x}

d er i v a t i v e x^{3} - 8 x^{2}

\int_{- 1}^{1} (1 - x^{2}) d x

d er i v a t i v e f (x) = x^{2} x - 5 x

What is the derivative of e^{{g}(x(x^3)-2x}) ?
The derivative of e^{{g}(x(x^3)-2x}) is e^{{g}(x)x^3-2x}(derivative of {g}(x)x^3+3x^2{g}(x)-2)
What is the first derivative of e^{{g}(x(x^3)-2x}) ?
The first derivative of e^{{g}(x(x^3)-2x}) is e^{{g}(x)x^3-2x}(derivative of {g}(x)x^3+3x^2{g}(x)-2)