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

The derivative of (x^2+5)^2(x-5) is 5x^4-20x^3+30x^2-100x+25

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

The first derivative of (x^2+5)^2(x-5) is 5x^4-20x^3+30x^2-100x+25

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derivative of

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

5 x^{4} - 20 x^{3} + 30 x^{2} - 100 x + 25

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} ((x^{2} + 5)^{2}) = 4 x (x^{2} + 5)

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

= 4 x (x^{2} + 5) (x - 5) + 1 \cdot (x^{2} + 5)^{2}

Simplify

4 x (x^{2} + 5) (x - 5) + 1 \cdot (x^{2} + 5)^{2} : 5 x^{4} - 20 x^{3} + 30 x^{2} - 100 x + 25

= 5 x^{4} - 20 x^{3} + 30 x^{2} - 100 x + 25

\int 6 x^{2} + 16 x - 10 d x

\frac{\partial}{\partial y} (sin (π (5 x - 2 y)))

\int cosh^{2} (x) d x

\int y e^{- 3 y} d y

\frac{d}{d x} ((x^{2} + 3 x)^{4})

What is the derivative of (x^2+5)^2(x-5) ?
The derivative of (x^2+5)^2(x-5) is 5x^4-20x^3+30x^2-100x+25
What is the first derivative of (x^2+5)^2(x-5) ?
The first derivative of (x^2+5)^2(x-5) is 5x^4-20x^3+30x^2-100x+25