What is the derivative of 5xcos(x) ?

The derivative of 5xcos(x) is 5(cos(x)-xsin(x))

What is the first derivative of 5xcos(x) ?

The first derivative of 5xcos(x) is 5(cos(x)-xsin(x))

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

5 (cos (x) - x sin (x))

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

f = x, g = cos (x)

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

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

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

= 5 (1 \cdot cos (x) + (- sin (x)) x)

Simplify

= 5 (cos (x) - x sin (x))

x \to 0 + lim (3 - x)

\frac{d}{d x} (3 sin (x) + 3 cos (x))

\int ln (x + 16) d x

\frac{d}{d x} (ln (x) \cdot ln (x))

\int_{- 1}^{1} \frac{x}{x ^{2} + x - 6} d x

What is the derivative of 5xcos(x) ?
The derivative of 5xcos(x) is 5(cos(x)-xsin(x))
What is the first derivative of 5xcos(x) ?
The first derivative of 5xcos(x) is 5(cos(x)-xsin(x))