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Popular >

derivative of 4sin(x+4xcos(x))

Solution

\frac{d}{d x} (4 sin (x) + 4 x cos (x))

Solution

8 cos (x) - 4 x sin (x)

Solution steps

\frac{d}{d x} (4 sin (x) + 4 x cos (x))

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (4 sin (x)) + \frac{d}{d x} (4 x cos (x))

\frac{d}{d x} (4 sin (x)) = 4 cos (x)

\frac{d}{d x} (4 x cos (x)) = 4 (cos (x) - x sin (x))

= 4 cos (x) + 4 (cos (x) - x sin (x))

Simplify

4 cos (x) + 4 (cos (x) - x sin (x)) : 8 cos (x) - 4 x sin (x)

= 8 cos (x) - 4 x sin (x)

Graph

Popular Examples

sum from n=0 to infinity of (4/7)^n

n = 0 \sum \infty (\frac{4}{7})^{n}

(dy)/(dx)=(((1+y)^2))/((1+x)^3),y(1)=0

\frac{d y}{d x} = \frac{( ( 1 + y ) ^{2} )}{( 1 + x ) ^{3}}, y (1) = 0

(\partial)/(\partial x)(ln(x+5y+8z))

\frac{\partial}{\partial x} (ln (x + 5 y + 8 z))

limit as t approaches-3 of e^t

t \to - 3 lim (e^{t})

(\partial)/(\partial y)(x/(x^4-y^3))

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

Frequently Asked Questions (FAQ)

What is the derivative of 4sin(x+4xcos(x)) ?
The derivative of 4sin(x+4xcos(x)) is 8cos(x)-4xsin(x)
What is the first derivative of 4sin(x+4xcos(x)) ?
The first derivative of 4sin(x+4xcos(x)) is 8cos(x)-4xsin(x)