What is the derivative of 1/2 x^2sqrt(36-x^2) ?

The derivative of 1/2 x^2sqrt(36-x^2) is (72x-3x^3)/(2sqrt(36-x^2))

What is the first derivative of 1/2 x^2sqrt(36-x^2) ?

The first derivative of 1/2 x^2sqrt(36-x^2) is (72x-3x^3)/(2sqrt(36-x^2))

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\frac{d}{d x} (\frac{1}{2} x^{2} 36 - x^{2})

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

Solution steps

\frac{d}{d x} (\frac{1}{2} x^{2} 36 - x^{2})

Take the constant out:

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

= \frac{1}{2} \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{1}{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}}

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

Simplify

\frac{1}{2} (2 x 36 - x^{2} + (- \frac{x}{36 - x ^{2}}) x^{2}) : \frac{72 x - 3 x ^{3}}{2 36 - x ^{2}}

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

n = 0 \sum \infty 2^{n} 1^{n}

\int \frac{1}{( x ^{2} + 1 ) ^{2}} d x

\int x cos^{2} (4 x) d x

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

- 45 y^{^{''}} + 35 y^{^{'}} = 0, y (2) = 2, y^{^{'}} (- 1) = - 1

What is the derivative of 1/2 x^2sqrt(36-x^2) ?
The derivative of 1/2 x^2sqrt(36-x^2) is (72x-3x^3)/(2sqrt(36-x^2))
What is the first derivative of 1/2 x^2sqrt(36-x^2) ?
The first derivative of 1/2 x^2sqrt(36-x^2) is (72x-3x^3)/(2sqrt(36-x^2))