What is the derivative of asqrt(b^2-x^2) ?

The derivative of asqrt(b^2-x^2) is -(ax)/(sqrt(b^2-x^2))

What is the first derivative of asqrt(b^2-x^2) ?

The first derivative of asqrt(b^2-x^2) is -(ax)/(sqrt(b^2-x^2))

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\frac{d}{d x} (a b^{2} - x^{2})

- \frac{a x}{b ^{2} - x ^{2}}

Solution steps

\frac{d}{d x} (a b^{2} - x^{2})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= a \frac{d}{d x} (b^{2} - x^{2})

Apply the chain rule:

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

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

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

= a \frac{1}{2 b ^{2} - x ^{2}} (- 2 x)

Simplify

a \frac{1}{2 b ^{2} - x ^{2}} (- 2 x) : - \frac{a x}{b ^{2} - x ^{2}}

= - \frac{a x}{b ^{2} - x ^{2}}

\frac{d}{d x} (x - \frac{1}{x})

\int \frac{2 + x ^{2}}{4 - x ^{4}} d x

\int 49 tan^{5} (x) sec^{4} (x) d x

h \to 0 + lim (2 + h)

\frac{x d y}{d x} = y^{2} - y

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