What is the derivative of (bsqrt(a^2-x^2)/a) ?

The derivative of (bsqrt(a^2-x^2)/a) is -(bx)/(asqrt(a^2-x^2))

What is the first derivative of (bsqrt(a^2-x^2)/a) ?

The first derivative of (bsqrt(a^2-x^2)/a) is -(bx)/(asqrt(a^2-x^2))

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

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

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

x \to 3 lim (2 x + 5)

\frac{d}{d x} (\frac{4}{x ^{11}})

(y + x cot (\frac{y}{x})) d x - x d y = 0

x \to \infty lim (x \cdot 2^{x})

x \to 4 + lim (\frac{3 x}{4} + 2)

What is the derivative of (bsqrt(a^2-x^2)/a) ?
The derivative of (bsqrt(a^2-x^2)/a) is -(bx)/(asqrt(a^2-x^2))
What is the first derivative of (bsqrt(a^2-x^2)/a) ?
The first derivative of (bsqrt(a^2-x^2)/a) is -(bx)/(asqrt(a^2-x^2))