What is the derivative of f(x)=x^{14}cos(x) ?

The derivative of f(x)=x^{14}cos(x) is 14x^{13}cos(x)-x^{14}sin(x)

What is the first derivative of f(x)=x^{14}cos(x) ?

The first derivative of f(x)=x^{14}cos(x) is 14x^{13}cos(x)-x^{14}sin(x)

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derivative of

f (x) = x^{14} cos (x)

14 x^{13} cos (x) - x^{14} sin (x)

Solution steps

\frac{d}{d x} (x^{14} cos (x))

Apply the Product Rule:

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

f = x^{14}, g = cos (x)

= \frac{d}{d x} (x^{14}) cos (x) + \frac{d}{d x} (cos (x)) x^{14}

\frac{d}{d x} (x^{14}) = 14 x^{13}

\frac{d}{d x} (cos (x)) = - sin (x)

= 14 x^{13} cos (x) + (- sin (x)) x^{14}

Simplify

= 14 x^{13} cos (x) - x^{14} sin (x)

What is the derivative of f(x)=x^{14}cos(x) ?
The derivative of f(x)=x^{14}cos(x) is 14x^{13}cos(x)-x^{14}sin(x)
What is the first derivative of f(x)=x^{14}cos(x) ?
The first derivative of f(x)=x^{14}cos(x) is 14x^{13}cos(x)-x^{14}sin(x)