What is the derivative of (x^2-2x+5)sqrt(25-x^2) ?

The derivative of (x^2-2x+5)sqrt(25-x^2) is (-3x^3+4x^2+45x-50)/(sqrt(25-x^2))

What is the first derivative of (x^2-2x+5)sqrt(25-x^2) ?

The first derivative of (x^2-2x+5)sqrt(25-x^2) is (-3x^3+4x^2+45x-50)/(sqrt(25-x^2))

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derivative of

(x^{2} - 2 x + 5) 25 - x^{2}

\frac{- 3 x ^{3} + 4 x ^{2} + 45 x - 50}{25 - x ^{2}}

Solution steps

\frac{d}{d x} ((x^{2} - 2 x + 5) 25 - x^{2})

Apply the Product Rule:

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

f = x^{2} - 2 x + 5, g = 25 - x^{2}

= \frac{d}{d x} (x^{2} - 2 x + 5) 25 - x^{2} + \frac{d}{d x} (25 - x^{2}) (x^{2} - 2 x + 5)

\frac{d}{d x} (x^{2} - 2 x + 5) = 2 x - 2

\frac{d}{d x} (25 - x^{2}) = - \frac{x}{25 - x ^{2}}

= (2 x - 2) 25 - x^{2} + (- \frac{x}{25 - x ^{2}}) (x^{2} - 2 x + 5)

Simplify

(2 x - 2) 25 - x^{2} + (- \frac{x}{25 - x ^{2}}) (x^{2} - 2 x + 5) : \frac{- 3 x ^{3} + 4 x ^{2} + 45 x - 50}{25 - x ^{2}}

= \frac{- 3 x ^{3} + 4 x ^{2} + 45 x - 50}{25 - x ^{2}}

What is the derivative of (x^2-2x+5)sqrt(25-x^2) ?
The derivative of (x^2-2x+5)sqrt(25-x^2) is (-3x^3+4x^2+45x-50)/(sqrt(25-x^2))
What is the first derivative of (x^2-2x+5)sqrt(25-x^2) ?
The first derivative of (x^2-2x+5)sqrt(25-x^2) is (-3x^3+4x^2+45x-50)/(sqrt(25-x^2))