What is the derivative of (x^2+7(5-x)) ?

The derivative of (x^2+7(5-x)) is 10x-3x^2-7

What is the first derivative of (x^2+7(5-x)) ?

The first derivative of (x^2+7(5-x)) is 10x-3x^2-7

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\frac{d}{d x} ((x^{2} + 7) (5 - x))

10 x - 3 x^{2} - 7

Solution steps

\frac{d}{d x} ((x^{2} + 7) (5 - x))

Apply the Product Rule:

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

f = x^{2} + 7, g = 5 - x

= \frac{d}{d x} (x^{2} + 7) (5 - x) + \frac{d}{d x} (5 - x) (x^{2} + 7)

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

\frac{d}{d x} (5 - x) = - 1

= 2 x (5 - x) + (- 1) (x^{2} + 7)

Simplify

2 x (5 - x) + (- 1) (x^{2} + 7) : 10 x - 3 x^{2} - 7

= 10 x - 3 x^{2} - 7

\int 3 - x^{2} d x

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

\frac{d}{d y} (sin (y) - y sin (x))

- 4 (x - 4)^{3}

\int cos (3 x) sin^{3} (3 x) d x

What is the derivative of (x^2+7(5-x)) ?
The derivative of (x^2+7(5-x)) is 10x-3x^2-7
What is the first derivative of (x^2+7(5-x)) ?
The first derivative of (x^2+7(5-x)) is 10x-3x^2-7