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Popular >

derivative of e^{6x}cos(bx)

Solution

\frac{d}{d x} (e^{6 x} cos (b x))

Solution

6 e^{6 x} cos (b x) - b e^{6 x} sin (b x)

Solution steps

\frac{d}{d x} (e^{6 x} cos (b x))

Apply the Product Rule:

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

f = e^{6 x}, g = cos (b x)

= \frac{d}{d x} (e^{6 x}) cos (b x) + \frac{d}{d x} (cos (b x)) e^{6 x}

\frac{d}{d x} (e^{6 x}) = e^{6 x} \cdot 6

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

= e^{6 x} \cdot 6 cos (b x) + (- sin (b x) b) e^{6 x}

Simplify

= 6 e^{6 x} cos (b x) - b e^{6 x} sin (b x)

Popular Examples

derivative of (x+y)^2-4x+y+10 derivative of

(x + y)^{2} - 4 x + y + 10

integral from 0 to pi of 2cos^2(pi/2)

\int_{0}^{π} 2 cos^{2} (\frac{π}{2}) d x

integral of 2/7 x^2+1

\int \frac{2}{7} x^{2} + 1 d x

tangent of f(x)=3x^2,(-1,3)tangent of

f (x) = 3 x^{2}, (- 1, 3)

laplacetransform g(t)=sqrt(t)laplace transform

g (t) = t

Frequently Asked Questions (FAQ)

What is the derivative of e^{6x}cos(bx) ?
The derivative of e^{6x}cos(bx) is 6e^{6x}cos(bx)-be^{6x}sin(bx)
What is the first derivative of e^{6x}cos(bx) ?
The first derivative of e^{6x}cos(bx) is 6e^{6x}cos(bx)-be^{6x}sin(bx)