What is the derivative of x^2sqrt(36-x^2) ?

The derivative of x^2sqrt(36-x^2) is (-3x^3+72x)/(sqrt(36-x^2))

What is the first derivative of x^2sqrt(36-x^2) ?

The first derivative of x^2sqrt(36-x^2) is (-3x^3+72x)/(sqrt(36-x^2))

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derivative of

x^{2} 36 - x^{2}

\frac{- 3 x ^{3} + 72 x}{36 - x ^{2}}

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

2 x 36 - x^{2} + (- \frac{x}{36 - x ^{2}}) x^{2} : \frac{- 3 x ^{3} + 72 x}{36 - x ^{2}}

= \frac{- 3 x ^{3} + 72 x}{36 - x ^{2}}

x^{2} d y - 2 x y d x = x^{4} cos (2 x) d x

\int \frac{2 x ^{2} + 7 x - 3}{x - 2} d x

ln (arctan (x))

(t + e^{t}) (6 - t)

y^{^{''}} + 5 y^{^{'}} + 6 y = 6

What is the derivative of x^2sqrt(36-x^2) ?
The derivative of x^2sqrt(36-x^2) is (-3x^3+72x)/(sqrt(36-x^2))
What is the first derivative of x^2sqrt(36-x^2) ?
The first derivative of x^2sqrt(36-x^2) is (-3x^3+72x)/(sqrt(36-x^2))