What is the derivative of y=sqrt(3)x(x+2)^3 ?

The derivative of y=sqrt(3)x(x+2)^3 is sqrt(3)((x+2)^3+3x(x+2)^2)

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

The first derivative of y=sqrt(3)x(x+2)^3 is sqrt(3)((x+2)^3+3x(x+2)^2)

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derivative of

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

\frac{d x}{d x} = 1

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

= 3 (1 \cdot (x + 2)^{3} + 3 (x + 2)^{2} x)

Simplify

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

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

\int - 2 cos (6 x) d x

f (x) = 8 x^{15} - 6 x^{3} + 1

\frac{d y}{d t} = y^{2} - y

x^{3} - 10 x, 15 x

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