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Popular >

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

Solution

derivative of

y = (x - 1)^{3} (x + 2)^{4}

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of y=(x-1)^3(x+2)^4 ?
The derivative of y=(x-1)^3(x+2)^4 is 3(x-1)^2(x+2)^4+4(x+2)^3(x-1)^3
What is the first derivative of y=(x-1)^3(x+2)^4 ?
The first derivative of y=(x-1)^3(x+2)^4 is 3(x-1)^2(x+2)^4+4(x+2)^3(x-1)^3