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Popular >

derivative of y=4sqrt(9-x^2)

Solution

derivative of

y = 4 9 - x^{2}

Solution

- \frac{4 x}{9 - x ^{2}}

Solution steps

\frac{d}{d x} (4 9 - x^{2})

Take the constant out:

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

= 4 \frac{d}{d x} (9 - x^{2})

Apply the chain rule:

\frac{1}{2 9 - x ^{2}} \frac{d}{d x} (9 - x^{2})

= \frac{1}{2 9 - x ^{2}} \frac{d}{d x} (9 - x^{2})

\frac{d}{d x} (9 - x^{2}) = - 2 x

= 4 \cdot \frac{1}{2 9 - x ^{2}} (- 2 x)

Simplify

4 \cdot \frac{1}{2 9 - x ^{2}} (- 2 x) : - \frac{4 x}{9 - x ^{2}}

= - \frac{4 x}{9 - x ^{2}}

Popular Examples

derivative of (x^2-1^{-1})

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

derivative of f(x)=sqrt(9-16x)derivative of

f (x) = 9 - 16 x

integral of (8x^7+9)sqrt(x^8+9x)

\int (8 x^{7} + 9) x^{8} + 9 x d x

tangent of y= 8/(x^2)tangent of

y = \frac{8}{x ^{2}}

derivative of 16e^{2x}

\frac{d}{d x} (16 e^{2 x})

Frequently Asked Questions (FAQ)

What is the derivative of y=4sqrt(9-x^2) ?
The derivative of y=4sqrt(9-x^2) is -(4x)/(sqrt(9-x^2))
What is the first derivative of y=4sqrt(9-x^2) ?
The first derivative of y=4sqrt(9-x^2) is -(4x)/(sqrt(9-x^2))