What is the derivative of sqrt(2-3x^2) ?

The derivative of sqrt(2-3x^2) is -(3x)/(sqrt(2-3x^2))

What is the first derivative of sqrt(2-3x^2) ?

The first derivative of sqrt(2-3x^2) is -(3x)/(sqrt(2-3x^2))

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

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

Solution steps

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

Apply the chain rule:

\frac{1}{2 2 - 3 x ^{2}} \frac{d}{d x} (2 - 3 x^{2})

= \frac{1}{2 2 - 3 x ^{2}} \frac{d}{d x} (2 - 3 x^{2})

\frac{d}{d x} (2 - 3 x^{2}) = - 6 x

= \frac{1}{2 2 - 3 x ^{2}} (- 6 x)

Simplify

\frac{1}{2 2 - 3 x ^{2}} (- 6 x) : - \frac{3 x}{2 - 3 x ^{2}}

= - \frac{3 x}{2 - 3 x ^{2}}

What is the derivative of sqrt(2-3x^2) ?
The derivative of sqrt(2-3x^2) is -(3x)/(sqrt(2-3x^2))
What is the first derivative of sqrt(2-3x^2) ?
The first derivative of sqrt(2-3x^2) is -(3x)/(sqrt(2-3x^2))