What is the derivative of x(x^3+6^4) ?

The derivative of x(x^3+6^4) is (x^3+6)^4+12x^3(x^3+6)^3

What is the first derivative of x(x^3+6^4) ?

The first derivative of x(x^3+6^4) is (x^3+6)^4+12x^3(x^3+6)^3

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\frac{d}{d x} (x (x^{3} + 6)^{4})

(x^{3} + 6)^{4} + 12 x^{3} (x^{3} + 6)^{3}

Solution steps

\frac{d}{d x} (x (x^{3} + 6)^{4})

Apply the Product Rule:

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

f = x, g = (x^{3} + 6)^{4}

= \frac{d x}{d x} (x^{3} + 6)^{4} + \frac{d}{d x} ((x^{3} + 6)^{4}) x

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

\frac{d}{d x} ((x^{3} + 6)^{4}) = 12 x^{2} (x^{3} + 6)^{3}

= 1 \cdot (x^{3} + 6)^{4} + 12 x^{2} (x^{3} + 6)^{3} x

Simplify

1 \cdot (x^{3} + 6)^{4} + 12 x^{2} (x^{3} + 6)^{3} x : (x^{3} + 6)^{4} + 12 x^{3} (x^{3} + 6)^{3}

= (x^{3} + 6)^{4} + 12 x^{3} (x^{3} + 6)^{3}

\frac{1}{x - e}

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What is the derivative of x(x^3+6^4) ?
The derivative of x(x^3+6^4) is (x^3+6)^4+12x^3(x^3+6)^3
What is the first derivative of x(x^3+6^4) ?
The first derivative of x(x^3+6^4) is (x^3+6)^4+12x^3(x^3+6)^3