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Popular >

derivative of (x-1sin(x))

Solution

\frac{d}{d x} ((x - 1) sin (x))

Solution

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

Solution steps

\frac{d}{d x} ((x - 1) sin (x))

Apply the Product Rule:

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

f = x - 1, g = sin (x)

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

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

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

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

Simplify

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

Popular Examples

(\partial)/(\partial x)(ln(e^x+e^y))

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

d/(dy)(1+ye^{xy})

\frac{d}{d y} (1 + y e^{x y})

integral of xtan(pix)

\int x tan (π x) d x

(\partial)/(\partial x)(sin(4x-2y))

\frac{\partial}{\partial x} (sin (4 x - 2 y))

derivative of (sqrt(x)/(e^x+1))

\frac{d}{d x} (\frac{x}{e ^{x} + 1})

Frequently Asked Questions (FAQ)

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