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Popular >

derivative of (x-cos(x)sin(x))

Solution

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

Solution

(1 + sin (x)) sin (x) + cos (x) (x - cos (x))

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} (x - cos (x)) = 1 + sin (x)

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

= (1 + sin (x)) sin (x) + cos (x) (x - cos (x))

Graph

Popular Examples

tangent of 4x^3-5x+3 tangent of

4 x^{3} - 5 x + 3

limit as x approaches 0 of (1/x)sin(x)

x \to 0 lim ((\frac{1}{x}) sin (x))

area y= 25/2-(x^2)/2 ,(-5,5)area

y = \frac{25}{2} - \frac{x ^{2}}{2}, (- 5, 5)

derivative of 5-3x

\frac{d}{d x} (5 - 3 x)

laplacetransform 20t^3 laplace transform

20 t^{3}

Frequently Asked Questions (FAQ)

What is the derivative of (x-cos(x)sin(x)) ?
The derivative of (x-cos(x)sin(x)) is (1+sin(x))sin(x)+cos(x)(x-cos(x))
What is the first derivative of (x-cos(x)sin(x)) ?
The first derivative of (x-cos(x)sin(x)) is (1+sin(x))sin(x)+cos(x)(x-cos(x))