What is the derivative of f(x)=5x(sin(x)+cos(x)) ?

The derivative of f(x)=5x(sin(x)+cos(x)) is 5(sin(x)+cos(x)+x(cos(x)-sin(x)))

What is the first derivative of f(x)=5x(sin(x)+cos(x)) ?

The first derivative of f(x)=5x(sin(x)+cos(x)) is 5(sin(x)+cos(x)+x(cos(x)-sin(x)))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

f (x) = 5 x (sin (x) + cos (x))

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

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

f = x, g = sin (x) + cos (x)

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

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

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

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

Simplify

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

\int sin (π + 2 y) - sin (2 y) d y

\frac{\partial}{\partial y} (x y e^{y} + e^{y} sin (x))

\frac{\partial}{\partial x} (16 - x^{2} - y^{2})

y = e^{- 2 x} + 1, y = 0, x = 0, x = 3

\frac{\partial}{\partial t} (3 e^{s i n (x + 4 c t)})

What is the derivative of f(x)=5x(sin(x)+cos(x)) ?
The derivative of f(x)=5x(sin(x)+cos(x)) is 5(sin(x)+cos(x)+x(cos(x)-sin(x)))
What is the first derivative of f(x)=5x(sin(x)+cos(x)) ?
The first derivative of f(x)=5x(sin(x)+cos(x)) is 5(sin(x)+cos(x)+x(cos(x)-sin(x)))