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Popular >

derivative of (3x-1^5(2x+3)^4)

Solution

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

Solution

15 (3 x - 1)^{4} (2 x + 3)^{4} + 8 (2 x + 3)^{3} (3 x - 1)^{5}

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} ((3 x - 1)^{5}) = 15 (3 x - 1)^{4}

\frac{d}{d x} ((2 x + 3)^{4}) = 8 (2 x + 3)^{3}

= 15 (3 x - 1)^{4} (2 x + 3)^{4} + 8 (2 x + 3)^{3} (3 x - 1)^{5}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of (3x-1^5(2x+3)^4) ?
The derivative of (3x-1^5(2x+3)^4) is 15(3x-1)^4(2x+3)^4+8(2x+3)^3(3x-1)^5
What is the first derivative of (3x-1^5(2x+3)^4) ?
The first derivative of (3x-1^5(2x+3)^4) is 15(3x-1)^4(2x+3)^4+8(2x+3)^3(3x-1)^5