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

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

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

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

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derivative of

y = x^{5} cos (x)

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

Solution steps

\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)

= \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)

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

Simplify

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

\frac{d}{d x} (a (x + 1) (x - r))

t y^{^{'}} + y = 0

\frac{d x}{d t} = x - 4

\int_{1}^{\infty} \frac{x}{x ^{4} + 1} d x

y = \frac{1 + 2 x}{3 + x}, (2, 1)

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