What is the derivative of 5(2-x^3^4) ?

The derivative of 5(2-x^3^4) is -60x^2(2-x^3)^3

What is the first derivative of 5(2-x^3^4) ?

The first derivative of 5(2-x^3^4) is -60x^2(2-x^3)^3

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\frac{d}{d x} (5 (2 - x^{3})^{4})

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

Solution steps

\frac{d}{d x} (5 (2 - x^{3})^{4})

Take the constant out:

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

= 5 \frac{d}{d x} ((2 - x^{3})^{4})

Apply the chain rule:

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

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

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

= 5 \cdot 4 (2 - x^{3})^{3} (- 3 x^{2})

Simplify

= - 60 x^{2} (2 - x^{3})^{3}

What is the derivative of 5(2-x^3^4) ?
The derivative of 5(2-x^3^4) is -60x^2(2-x^3)^3
What is the first derivative of 5(2-x^3^4) ?
The first derivative of 5(2-x^3^4) is -60x^2(2-x^3)^3