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

The derivative of (5x+2)^4(2x-3)^8 is 20(5x+2)^3(2x-3)^8+16(2x-3)^7(5x+2)^4

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

The first derivative of (5x+2)^4(2x-3)^8 is 20(5x+2)^3(2x-3)^8+16(2x-3)^7(5x+2)^4

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derivative of

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

20 (5 x + 2)^{3} (2 x - 3)^{8} + 16 (2 x - 3)^{7} (5 x + 2)^{4}

Solution steps

\frac{d}{d x} ((5 x + 2)^{4} (2 x - 3)^{8})

Apply the Product Rule:

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

f = (5 x + 2)^{4}, g = (2 x - 3)^{8}

= \frac{d}{d x} ((5 x + 2)^{4}) (2 x - 3)^{8} + \frac{d}{d x} ((2 x - 3)^{8}) (5 x + 2)^{4}

\frac{d}{d x} ((5 x + 2)^{4}) = 20 (5 x + 2)^{3}

\frac{d}{d x} ((2 x - 3)^{8}) = 16 (2 x - 3)^{7}

= 20 (5 x + 2)^{3} (2 x - 3)^{8} + 16 (2 x - 3)^{7} (5 x + 2)^{4}

3 \cdot \frac{d y}{d x} + 12 y = 4

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x \to 1.2 lim (\frac{1}{x - 2})

\int \frac{( x ^{2} - x + 6 )}{x ^{3} + 3 x} d x

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What is the derivative of (5x+2)^4(2x-3)^8 ?
The derivative of (5x+2)^4(2x-3)^8 is 20(5x+2)^3(2x-3)^8+16(2x-3)^7(5x+2)^4
What is the first derivative of (5x+2)^4(2x-3)^8 ?
The first derivative of (5x+2)^4(2x-3)^8 is 20(5x+2)^3(2x-3)^8+16(2x-3)^7(5x+2)^4