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

The derivative of (x-3^3(x+4)(x^2+1)) is 3(x-3)^2(x+4)(x^2+1)+(3x^2+8x+1)(x-3)^3

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

The first derivative of (x-3^3(x+4)(x^2+1)) is 3(x-3)^2(x+4)(x^2+1)+(3x^2+8x+1)(x-3)^3

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

3 (x - 3)^{2} (x + 4) (x^{2} + 1) + (3 x^{2} + 8 x + 1) (x - 3)^{3}

Solution steps

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

Apply the Product Rule:

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

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

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

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

\frac{d}{d x} ((x + 4) (x^{2} + 1)) = 3 x^{2} + 8 x + 1

= 3 (x - 3)^{2} (x + 4) (x^{2} + 1) + (3 x^{2} + 8 x + 1) (x - 3)^{3}

y = x - x^{3}

\int (cos (x))^{5} d x

\frac{\partial}{\partial y} (\frac{x - y}{x + z})

\frac{d y}{d x} = 7 x y

x \to 0 lim (3 x + 4)

What is the derivative of (x-3^3(x+4)(x^2+1)) ?
The derivative of (x-3^3(x+4)(x^2+1)) is 3(x-3)^2(x+4)(x^2+1)+(3x^2+8x+1)(x-3)^3
What is the first derivative of (x-3^3(x+4)(x^2+1)) ?
The first derivative of (x-3^3(x+4)(x^2+1)) is 3(x-3)^2(x+4)(x^2+1)+(3x^2+8x+1)(x-3)^3