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Popular >

derivative of x-x^3sin(x)

Solution

\frac{d}{d x} (x - x^{3} sin (x))

Solution

1 - 3 x^{2} sin (x) - x^{3} cos (x)

Solution steps

\frac{d}{d x} (x - x^{3} sin (x))

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d x}{d x} - \frac{d}{d x} (x^{3} sin (x))

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

\frac{d}{d x} (x^{3} sin (x)) = 3 x^{2} sin (x) + cos (x) x^{3}

= 1 - (3 x^{2} sin (x) + cos (x) x^{3})

Simplify

1 - (3 x^{2} sin (x) + cos (x) x^{3}) : 1 - 3 x^{2} sin (x) - x^{3} cos (x)

= 1 - 3 x^{2} sin (x) - x^{3} cos (x)

Graph

Popular Examples

inverse oflaplace s/((s^2+1)(s^2+2s+2))inverse laplace

\frac{s}{( s ^{2} + 1 ) ( s ^{2} + 2 s + 2 )}

(dy)/(dx)=y(xy^6+3)

\frac{d y}{d x} = y (x y^{6} + 3)

area 16x,x^3,[-4,4]area

16 x, x^{3}, [- 4, 4]

(dy)/(dx)=(x+y+6)^2

\frac{d y}{d x} = (x + y + 6)^{2}

integral of (6xy^2)

\int (6 x y^{2}) d z

Frequently Asked Questions (FAQ)

What is the derivative of x-x^3sin(x) ?
The derivative of x-x^3sin(x) is 1-3x^2sin(x)-x^3cos(x)
What is the first derivative of x-x^3sin(x) ?
The first derivative of x-x^3sin(x) is 1-3x^2sin(x)-x^3cos(x)