What is the derivative of (x^2-7x+8)sqrt(25-x^2) ?

The derivative of (x^2-7x+8)sqrt(25-x^2) is (-3x^3+14x^2+42x-175)/(sqrt(25-x^2))

What is the first derivative of (x^2-7x+8)sqrt(25-x^2) ?

The first derivative of (x^2-7x+8)sqrt(25-x^2) is (-3x^3+14x^2+42x-175)/(sqrt(25-x^2))

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derivative of

(x^{2} - 7 x + 8) 25 - x^{2}

\frac{- 3 x ^{3} + 14 x ^{2} + 42 x - 175}{25 - x ^{2}}

Solution steps

\frac{d}{d x} ((x^{2} - 7 x + 8) 25 - x^{2})

Apply the Product Rule:

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

f = x^{2} - 7 x + 8, g = 25 - x^{2}

= \frac{d}{d x} (x^{2} - 7 x + 8) 25 - x^{2} + \frac{d}{d x} (25 - x^{2}) (x^{2} - 7 x + 8)

\frac{d}{d x} (x^{2} - 7 x + 8) = 2 x - 7

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

= (2 x - 7) 25 - x^{2} + (- \frac{x}{25 - x ^{2}}) (x^{2} - 7 x + 8)

Simplify

(2 x - 7) 25 - x^{2} + (- \frac{x}{25 - x ^{2}}) (x^{2} - 7 x + 8) : \frac{- 3 x ^{3} + 14 x ^{2} + 42 x - 175}{25 - x ^{2}}

= \frac{- 3 x ^{3} + 14 x ^{2} + 42 x - 175}{25 - x ^{2}}

\frac{d}{d x} (arcsec (x^{4}))

\frac{\partial}{\partial y} (\frac{3 x + 1}{x + 2})

y^{^{''}} + 4 y^{^{'}} + 5 y = 0, y (0) = 1, y^{^{'}} (0) = 2

\int \frac{1}{1 - 3 v} d v

x \to 9 lim (\frac{x ^{2}}{3} - \frac{3}{x})

What is the derivative of (x^2-7x+8)sqrt(25-x^2) ?
The derivative of (x^2-7x+8)sqrt(25-x^2) is (-3x^3+14x^2+42x-175)/(sqrt(25-x^2))
What is the first derivative of (x^2-7x+8)sqrt(25-x^2) ?
The first derivative of (x^2-7x+8)sqrt(25-x^2) is (-3x^3+14x^2+42x-175)/(sqrt(25-x^2))