What is the derivative of y=xsqrt(36-x^2) ?

The derivative of y=xsqrt(36-x^2) is (-2x^2+36)/(sqrt(36-x^2))

What is the first derivative of y=xsqrt(36-x^2) ?

The first derivative of y=xsqrt(36-x^2) is (-2x^2+36)/(sqrt(36-x^2))

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derivative of

y = x 36 - x^{2}

\frac{- 2 x ^{2} + 36}{36 - x ^{2}}

Solution steps

\frac{d}{d x} (x 36 - x^{2})

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = 36 - x^{2}

= \frac{d x}{d x} 36 - x^{2} + \frac{d}{d x} (36 - x^{2}) x

\frac{d x}{d x} = 1

\frac{d}{d x} (36 - x^{2}) = - \frac{x}{36 - x ^{2}}

= 1 \cdot 36 - x^{2} + (- \frac{x}{36 - x ^{2}}) x

Simplify

1 \cdot 36 - x^{2} + (- \frac{x}{36 - x ^{2}}) x : \frac{- 2 x ^{2} + 36}{36 - x ^{2}}

= \frac{- 2 x ^{2} + 36}{36 - x ^{2}}

x y^{^{'}} + 3 y = x^{4} - x

\int \frac{e ^{x}}{( 5 - e ^{x} ) ^{2}} d x

\int sin (x) e^{- s x} d x

\int \frac{1}{v ^{2} - v + 1} d v

f (x) = ln (\frac{x + 1}{x - 1})

What is the derivative of y=xsqrt(36-x^2) ?
The derivative of y=xsqrt(36-x^2) is (-2x^2+36)/(sqrt(36-x^2))
What is the first derivative of y=xsqrt(36-x^2) ?
The first derivative of y=xsqrt(36-x^2) is (-2x^2+36)/(sqrt(36-x^2))