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Popular >

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

Solution

derivative of

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Popular Examples

y^{^{'}} = y (x y^{3} + 2)

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\int e^{3 x} e^{x} d x

derivative of-sin(x-1)

\frac{d}{d x} (- sin (x) - 1)

(\partial)/(\partial x)(xln(xy-5))

\frac{\partial}{\partial x} (x ln (x y - 5))

limit as x approaches 3 of x^2+4

x \to 3 lim (x^{2} + 4)

Frequently Asked Questions (FAQ)

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