What is the derivative of (5x-3(2x+5)^2) ?

The derivative of (5x-3(2x+5)^2) is 60x^2+176x+65

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

The first derivative of (5x-3(2x+5)^2) is 60x^2+176x+65

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\frac{d}{d x} ((5 x - 3) (2 x + 5)^{2})

60 x^{2} + 176 x + 65

Solution steps

\frac{d}{d x} ((5 x - 3) (2 x + 5)^{2})

Apply the Product Rule:

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

f = 5 x - 3, g = (2 x + 5)^{2}

= \frac{d}{d x} (5 x - 3) (2 x + 5)^{2} + \frac{d}{d x} ((2 x + 5)^{2}) (5 x - 3)

\frac{d}{d x} (5 x - 3) = 5

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

= 5 (2 x + 5)^{2} + 4 (2 x + 5) (5 x - 3)

Simplify

5 (2 x + 5)^{2} + 4 (2 x + 5) (5 x - 3) : 60 x^{2} + 176 x + 65

= 60 x^{2} + 176 x + 65

What is the derivative of (5x-3(2x+5)^2) ?
The derivative of (5x-3(2x+5)^2) is 60x^2+176x+65
What is the first derivative of (5x-3(2x+5)^2) ?
The first derivative of (5x-3(2x+5)^2) is 60x^2+176x+65