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Popular >

derivative of f(x)=[(4x^2+3x)cos(x)]

Solution

derivative of

f (x) = [(4 x^{2} + 3 x) cos (x)]

Solution

cos (x) (8 x + 3) - sin (x) (4 x^{2} + 3 x)

Solution steps

\frac{d}{d x} (((4 x^{2} + 3 x) cos (x)))

Apply the Product Rule:

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

f = 4 x^{2} + 3 x, g = cos (x)

= \frac{d}{d x} (4 x^{2} + 3 x) cos (x) + \frac{d}{d x} (cos (x)) (4 x^{2} + 3 x)

\frac{d}{d x} (4 x^{2} + 3 x) = 8 x + 3

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

= (8 x + 3) cos (x) + (- sin (x)) (4 x^{2} + 3 x)

Simplify

= cos (x) (8 x + 3) - sin (x) (4 x^{2} + 3 x)

Popular Examples

derivative of ((4z+4))/(3z^2+3z+3)derivative of

\frac{( 4 z + 4 )}{3 z ^{2} + 3 z + 3}

(dy)/(dx)=(xy)/(x^2+4),y(0)=6

\frac{d y}{d x} = \frac{x y}{x ^{2} + 4}, y (0) = 6

area 10,x,(x^2)/(40)area

10, x, \frac{x ^{2}}{40}

integral of 2cos(-4x)+1

\int 2 cos (- 4 x) + 1 d x

(\partial)/(\partial x)(x^2-4xy+3y^2)

\frac{\partial}{\partial x} (x^{2} - 4 x y + 3 y^{2})

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=[(4x^2+3x)cos(x)] ?
The derivative of f(x)=[(4x^2+3x)cos(x)] is cos(x)(8x+3)-sin(x)(4x^2+3x)
What is the first derivative of f(x)=[(4x^2+3x)cos(x)] ?
The first derivative of f(x)=[(4x^2+3x)cos(x)] is cos(x)(8x+3)-sin(x)(4x^2+3x)