What is the derivative of (3x+1)^4(5-2x)^3 ?

The derivative of (3x+1)^4(5-2x)^3 is 12(3x+1)^3(5-2x)^3-6(5-2x)^2(3x+1)^4

What is the first derivative of (3x+1)^4(5-2x)^3 ?

The first derivative of (3x+1)^4(5-2x)^3 is 12(3x+1)^3(5-2x)^3-6(5-2x)^2(3x+1)^4

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derivative of

(3 x + 1)^{4} (5 - 2 x)^{3}

12 (3 x + 1)^{3} (5 - 2 x)^{3} - 6 (5 - 2 x)^{2} (3 x + 1)^{4}

Solution steps

\frac{d}{d x} ((3 x + 1)^{4} (5 - 2 x)^{3})

Apply the Product Rule:

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

f = (3 x + 1)^{4}, g = (5 - 2 x)^{3}

= \frac{d}{d x} ((3 x + 1)^{4}) (5 - 2 x)^{3} + \frac{d}{d x} ((5 - 2 x)^{3}) (3 x + 1)^{4}

\frac{d}{d x} ((3 x + 1)^{4}) = 12 (3 x + 1)^{3}

\frac{d}{d x} ((5 - 2 x)^{3}) = - 6 (5 - 2 x)^{2}

= 12 (3 x + 1)^{3} (5 - 2 x)^{3} + (- 6 (5 - 2 x)^{2}) (3 x + 1)^{4}

Simplify

= 12 (3 x + 1)^{3} (5 - 2 x)^{3} - 6 (5 - 2 x)^{2} (3 x + 1)^{4}

What is the derivative of (3x+1)^4(5-2x)^3 ?
The derivative of (3x+1)^4(5-2x)^3 is 12(3x+1)^3(5-2x)^3-6(5-2x)^2(3x+1)^4
What is the first derivative of (3x+1)^4(5-2x)^3 ?
The first derivative of (3x+1)^4(5-2x)^3 is 12(3x+1)^3(5-2x)^3-6(5-2x)^2(3x+1)^4