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Popular >

derivative of y=3x^2(x-3)^3

Solution

derivative of

y = 3 x^{2} (x - 3)^{3}

Solution

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} (x^{2}) = 2 x

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

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

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Frequently Asked Questions (FAQ)

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