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

The derivative of x(x^2+3^3) is (x^2+3)^3+6x^2(x^2+3)^2

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

The first derivative of x(x^2+3^3) is (x^2+3)^3+6x^2(x^2+3)^2

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

(x^{2} + 3)^{3} + 6 x^{2} (x^{2} + 3)^{2}

Solution steps

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

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

\frac{d}{d x} ((x^{2} + 3)^{3}) = 6 x (x^{2} + 3)^{2}

= 1 \cdot (x^{2} + 3)^{3} + 6 x (x^{2} + 3)^{2} x

Simplify

1 \cdot (x^{2} + 3)^{3} + 6 x (x^{2} + 3)^{2} x : (x^{2} + 3)^{3} + 6 x^{2} (x^{2} + 3)^{2}

= (x^{2} + 3)^{3} + 6 x^{2} (x^{2} + 3)^{2}

y^{^{''}} + 9 y = 2 x^{2} - 5

x \to 1 lim (\frac{x ^{10} - 1}{x - 1})

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

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

x \to \infty lim (a^{- x})

What is the derivative of x(x^2+3^3) ?
The derivative of x(x^2+3^3) is (x^2+3)^3+6x^2(x^2+3)^2
What is the first derivative of x(x^2+3^3) ?
The first derivative of x(x^2+3^3) is (x^2+3)^3+6x^2(x^2+3)^2