What is the derivative of y=(x^2-2x+7)sqrt(25-x^2) ?

The derivative of y=(x^2-2x+7)sqrt(25-x^2) is (-3x^3+4x^2+43x-50)/(sqrt(25-x^2))

What is the first derivative of y=(x^2-2x+7)sqrt(25-x^2) ?

The first derivative of y=(x^2-2x+7)sqrt(25-x^2) is (-3x^3+4x^2+43x-50)/(sqrt(25-x^2))

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derivative of

y = (x^{2} - 2 x + 7) 25 - x^{2}

\frac{- 3 x ^{3} + 4 x ^{2} + 43 x - 50}{25 - x ^{2}}

Solution steps

\frac{d}{d x} ((x^{2} - 2 x + 7) 25 - x^{2})

Apply the Product Rule:

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

f = x^{2} - 2 x + 7, g = 25 - x^{2}

= \frac{d}{d x} (x^{2} - 2 x + 7) 25 - x^{2} + \frac{d}{d x} (25 - x^{2}) (x^{2} - 2 x + 7)

\frac{d}{d x} (x^{2} - 2 x + 7) = 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 + 7)

Simplify

(2 x - 2) 25 - x^{2} + (- \frac{x}{25 - x ^{2}}) (x^{2} - 2 x + 7) : \frac{- 3 x ^{3} + 4 x ^{2} + 43 x - 50}{25 - x ^{2}}

= \frac{- 3 x ^{3} + 4 x ^{2} + 43 x - 50}{25 - x ^{2}}

x \to 5 lim (x - 3)

\frac{\partial}{\partial x} (in (x + 2 y + 3 z))

x \to 1 lim (\frac{1}{1 - x})

\int \frac{( ln ( x ) ) ^{48}}{x} d x

ln (3 - 5 x)

What is the derivative of y=(x^2-2x+7)sqrt(25-x^2) ?
The derivative of y=(x^2-2x+7)sqrt(25-x^2) is (-3x^3+4x^2+43x-50)/(sqrt(25-x^2))
What is the first derivative of y=(x^2-2x+7)sqrt(25-x^2) ?
The first derivative of y=(x^2-2x+7)sqrt(25-x^2) is (-3x^3+4x^2+43x-50)/(sqrt(25-x^2))