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Popular >

derivative of (3x-5^7(5x+2)^4)

Solution

\frac{d}{d x} ((3 x - 5)^{7} (5 x + 2)^{4})

Solution

21 (3 x - 5)^{6} (5 x + 2)^{4} + 20 (5 x + 2)^{3} (3 x - 5)^{7}

Solution steps

\frac{d}{d x} ((3 x - 5)^{7} (5 x + 2)^{4})

Apply the Product Rule:

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

f = (3 x - 5)^{7}, g = (5 x + 2)^{4}

= \frac{d}{d x} ((3 x - 5)^{7}) (5 x + 2)^{4} + \frac{d}{d x} ((5 x + 2)^{4}) (3 x - 5)^{7}

\frac{d}{d x} ((3 x - 5)^{7}) = 21 (3 x - 5)^{6}

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

= 21 (3 x - 5)^{6} (5 x + 2)^{4} + 20 (5 x + 2)^{3} (3 x - 5)^{7}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of (3x-5^7(5x+2)^4) ?
The derivative of (3x-5^7(5x+2)^4) is 21(3x-5)^6(5x+2)^4+20(5x+2)^3(3x-5)^7
What is the first derivative of (3x-5^7(5x+2)^4) ?
The first derivative of (3x-5^7(5x+2)^4) is 21(3x-5)^6(5x+2)^4+20(5x+2)^3(3x-5)^7