What is the derivative of (x-5sin(x)) ?

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

What is the first derivative of (x-5sin(x)) ?

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

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\frac{d}{d x} ((x - 5) sin (x))

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

Solution steps

\frac{d}{d x} ((x - 5) sin (x))

Apply the Product Rule:

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

f = x - 5, g = sin (x)

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

\frac{d}{d x} (x - 5) = 1

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

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

Simplify

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

n = 0 \sum \infty \frac{1}{1. 5 ^{n}}

\int - x^{2} - 2 x d x

\int \frac{1}{e ^{6 x}} d x

\frac{d P}{d t} = 50 P - \frac{1}{10} P

\int \frac{cos ( 2 t )}{2} d t

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