What is the derivative of (2x+1^5(3x-2)^7) ?

The derivative of (2x+1^5(3x-2)^7) is 10(2x+1)^4(3x-2)^7+21(3x-2)^6(2x+1)^5

What is the first derivative of (2x+1^5(3x-2)^7) ?

The first derivative of (2x+1^5(3x-2)^7) is 10(2x+1)^4(3x-2)^7+21(3x-2)^6(2x+1)^5

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\frac{d}{d x} ((2 x + 1)^{5} (3 x - 2)^{7})

10 (2 x + 1)^{4} (3 x - 2)^{7} + 21 (3 x - 2)^{6} (2 x + 1)^{5}

Solution steps

\frac{d}{d x} ((2 x + 1)^{5} (3 x - 2)^{7})

Apply the Product Rule:

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

f = (2 x + 1)^{5}, g = (3 x - 2)^{7}

= \frac{d}{d x} ((2 x + 1)^{5}) (3 x - 2)^{7} + \frac{d}{d x} ((3 x - 2)^{7}) (2 x + 1)^{5}

\frac{d}{d x} ((2 x + 1)^{5}) = 10 (2 x + 1)^{4}

\frac{d}{d x} ((3 x - 2)^{7}) = 21 (3 x - 2)^{6}

= 10 (2 x + 1)^{4} (3 x - 2)^{7} + 21 (3 x - 2)^{6} (2 x + 1)^{5}

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\int_{0}^{t} \frac{1}{x} d x

What is the derivative of (2x+1^5(3x-2)^7) ?
The derivative of (2x+1^5(3x-2)^7) is 10(2x+1)^4(3x-2)^7+21(3x-2)^6(2x+1)^5
What is the first derivative of (2x+1^5(3x-2)^7) ?
The first derivative of (2x+1^5(3x-2)^7) is 10(2x+1)^4(3x-2)^7+21(3x-2)^6(2x+1)^5