What is the derivative of y=x^6cos(x) ?

The derivative of y=x^6cos(x) is 6x^5cos(x)-x^6sin(x)

What is the first derivative of y=x^6cos(x) ?

The first derivative of y=x^6cos(x) is 6x^5cos(x)-x^6sin(x)

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derivative of

y = x^{6} cos (x)

6 x^{5} cos (x) - x^{6} sin (x)

Solution steps

\frac{d}{d x} (x^{6} cos (x))

Apply the Product Rule:

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

f = x^{6}, g = cos (x)

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

\frac{d}{d x} (x^{6}) = 6 x^{5}

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

= 6 x^{5} cos (x) + (- sin (x)) x^{6}

Simplify

= 6 x^{5} cos (x) - x^{6} sin (x)

What is the derivative of y=x^6cos(x) ?
The derivative of y=x^6cos(x) is 6x^5cos(x)-x^6sin(x)
What is the first derivative of y=x^6cos(x) ?
The first derivative of y=x^6cos(x) is 6x^5cos(x)-x^6sin(x)