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Popular >

derivative of (6x+8(4x+9)^5)

Solution

\frac{d}{d x} ((6 x + 8) (4 x + 9)^{5})

Solution

6 (4 x + 9)^{5} + 20 (4 x + 9)^{4} (6 x + 8)

Solution steps

\frac{d}{d x} ((6 x + 8) (4 x + 9)^{5})

Apply the Product Rule:

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

f = 6 x + 8, g = (4 x + 9)^{5}

= \frac{d}{d x} (6 x + 8) (4 x + 9)^{5} + \frac{d}{d x} ((4 x + 9)^{5}) (6 x + 8)

\frac{d}{d x} (6 x + 8) = 6

\frac{d}{d x} ((4 x + 9)^{5}) = 20 (4 x + 9)^{4}

= 6 (4 x + 9)^{5} + 20 (4 x + 9)^{4} (6 x + 8)

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Frequently Asked Questions (FAQ)

What is the derivative of (6x+8(4x+9)^5) ?
The derivative of (6x+8(4x+9)^5) is 6(4x+9)^5+20(4x+9)^4(6x+8)
What is the first derivative of (6x+8(4x+9)^5) ?
The first derivative of (6x+8(4x+9)^5) is 6(4x+9)^5+20(4x+9)^4(6x+8)