What is the derivative of y=[x(x^5+4)^4] ?

The derivative of y=[x(x^5+4)^4] is (x^5+4)^4+20x^5(x^5+4)^3

What is the first derivative of y=[x(x^5+4)^4] ?

The first derivative of y=[x(x^5+4)^4] is (x^5+4)^4+20x^5(x^5+4)^3

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derivative of

y = [x (x^{5} + 4)^{4}]

(x^{5} + 4)^{4} + 20 x^{5} (x^{5} + 4)^{3}

Solution steps

\frac{d}{d x} ((x (x^{5} + 4)^{4}))

Apply the Product Rule:

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

f = x, g = (x^{5} + 4)^{4}

= \frac{d x}{d x} (x^{5} + 4)^{4} + \frac{d}{d x} ((x^{5} + 4)^{4}) x

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

\frac{d}{d x} ((x^{5} + 4)^{4}) = 20 x^{4} (x^{5} + 4)^{3}

= 1 \cdot (x^{5} + 4)^{4} + 20 x^{4} (x^{5} + 4)^{3} x

Simplify

1 \cdot (x^{5} + 4)^{4} + 20 x^{4} (x^{5} + 4)^{3} x : (x^{5} + 4)^{4} + 20 x^{5} (x^{5} + 4)^{3}

= (x^{5} + 4)^{4} + 20 x^{5} (x^{5} + 4)^{3}

What is the derivative of y=[x(x^5+4)^4] ?
The derivative of y=[x(x^5+4)^4] is (x^5+4)^4+20x^5(x^5+4)^3
What is the first derivative of y=[x(x^5+4)^4] ?
The first derivative of y=[x(x^5+4)^4] is (x^5+4)^4+20x^5(x^5+4)^3