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Popular >

derivative of f(x)=x^3cos(2x)

Solution

derivative of

f (x) = x^{3} cos (2 x)

Solution

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

Solution steps

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

Apply the Product Rule:

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

f = x^{3}, g = cos (2 x)

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

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

\frac{d}{d x} (cos (2 x)) = - sin (2 x) \cdot 2

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

Simplify

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

Popular Examples

x(dy)/(dx)=x^3+9x^3y

x \frac{d y}{d x} = x^{3} + 9 x^{3} y

y^{''}=6x,y(0)=1,y^'(0)=-1

y^{^{''}} = 6 x, y (0) = 1, y^{^{'}} (0) = - 1

integral of 1/(sqrt(49-64x^2))

\int \frac{1}{49 - 64 x ^{2}} d x

(\partial)/(\partial y)(x^4+x^2y+x+5)

\frac{\partial}{\partial y} (x^{4} + x^{2} y + x + 5)

derivative of sin((x-3)/(2x))derivative of

sin (\frac{x - 3}{2 x})

Frequently Asked Questions (FAQ)

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