What is the derivative of y=3x(4x-5)2 ?

The derivative of y=3x(4x-5)2 is 6(8x-5)

What is the first derivative of y=3x(4x-5)2 ?

The first derivative of y=3x(4x-5)2 is 6(8x-5)

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derivative of

y = 3 x (4 x - 5) 2

6 (8 x - 5)

Solution steps

\frac{d}{d x} (3 x (4 x - 5) \cdot 2)

Simplify

3 x (4 x - 5) \cdot 2 : 6 x (4 x - 5)

= \frac{d}{d x} (6 x (4 x - 5))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 6 \frac{d}{d x} (x (4 x - 5))

Apply the Product Rule:

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

f = x, g = 4 x - 5

= 6 (\frac{d x}{d x} (4 x - 5) + \frac{d}{d x} (4 x - 5) x)

\frac{d x}{d x} = 1

\frac{d}{d x} (4 x - 5) = 4

= 6 (1 \cdot (4 x - 5) + 4 x)

Simplify

= 6 (8 x - 5)

y = 7 x^{6}

x^{3} + 3 x + 5

x^{3} y^{3}

\frac{d}{d x} (a \cdot e^{2 x} + b \cdot e^{x} + c)

\frac{e ^{x} - 2}{2}

What is the derivative of y=3x(4x-5)2 ?
The derivative of y=3x(4x-5)2 is 6(8x-5)
What is the first derivative of y=3x(4x-5)2 ?
The first derivative of y=3x(4x-5)2 is 6(8x-5)