What is the derivative of f(x)=x(5x^5-1) ?

The derivative of f(x)=x(5x^5-1) is 30x^5-1

What is the first derivative of f(x)=x(5x^5-1) ?

The first derivative of f(x)=x(5x^5-1) is 30x^5-1

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derivative of

f (x) = x (5 x^{5} - 1)

30 x^{5} - 1

Solution steps

\frac{d}{d x} (x (5 x^{5} - 1))

Apply the Product Rule:

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

f = x, g = 5 x^{5} - 1

= \frac{d x}{d x} (5 x^{5} - 1) + \frac{d}{d x} (5 x^{5} - 1) x

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

\frac{d}{d x} (5 x^{5} - 1) = 25 x^{4}

= 1 \cdot (5 x^{5} - 1) + 25 x^{4} x

Simplify

1 \cdot (5 x^{5} - 1) + 25 x^{4} x : 30 x^{5} - 1

= 30 x^{5} - 1

What is the derivative of f(x)=x(5x^5-1) ?
The derivative of f(x)=x(5x^5-1) is 30x^5-1
What is the first derivative of f(x)=x(5x^5-1) ?
The first derivative of f(x)=x(5x^5-1) is 30x^5-1