What is the derivative of 9x^5cos(x) ?

The derivative of 9x^5cos(x) is 9(5x^4cos(x)-x^5sin(x))

What is the first derivative of 9x^5cos(x) ?

The first derivative of 9x^5cos(x) is 9(5x^4cos(x)-x^5sin(x))

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\frac{d}{d x} (9 x^{5} cos (x))

9 (5 x^{4} cos (x) - x^{5} sin (x))

Solution steps

\frac{d}{d x} (9 x^{5} cos (x))

Take the constant out:

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

= 9 \frac{d}{d x} (x^{5} cos (x))

Apply the Product Rule:

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

f = x^{5}, g = cos (x)

= 9 (\frac{d}{d x} (x^{5}) cos (x) + \frac{d}{d x} (cos (x)) x^{5})

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

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

= 9 (5 x^{4} cos (x) + (- sin (x)) x^{5})

Simplify

= 9 (5 x^{4} cos (x) - x^{5} sin (x))

What is the derivative of 9x^5cos(x) ?
The derivative of 9x^5cos(x) is 9(5x^4cos(x)-x^5sin(x))
What is the first derivative of 9x^5cos(x) ?
The first derivative of 9x^5cos(x) is 9(5x^4cos(x)-x^5sin(x))