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Popular >

derivative of axcos(x+bxsin(x))

Solution

\frac{d}{d x} (a x cos (x) + b x sin (x))

Solution

a (cos (x) - x sin (x)) + b (sin (x) + x cos (x))

Solution steps

\frac{d}{d x} (a x cos (x) + b x sin (x))

Apply the Sum/Difference Rule:

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

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

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

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

= a (cos (x) - x sin (x)) + b (sin (x) + x cos (x))

Popular Examples

implicit (dy)/(dx),y^4=x^7 implicit derivative

\frac{d y}{d x}, y^{4} = x^{7}

sec^2(pi/4)(pi/5)= 1/4 (dx)/(dt)

sec^{2} (\frac{π}{4}) (\frac{π}{5}) = \frac{1}{4} \frac{d x}{d t}

limit as x approaches 6+of sqrt(6-x)

x \to 6 + lim (6 - x)

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

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

derivative of 4x^2sin(x)tan(x)derivative of

4 x^{2} sin (x) tan (x)

Frequently Asked Questions (FAQ)

What is the derivative of axcos(x+bxsin(x)) ?
The derivative of axcos(x+bxsin(x)) is a(cos(x)-xsin(x))+b(sin(x)+xcos(x))
What is the first derivative of axcos(x+bxsin(x)) ?
The first derivative of axcos(x+bxsin(x)) is a(cos(x)-xsin(x))+b(sin(x)+xcos(x))