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Popular >

derivative of cos^3(5x+1)

Solution

\frac{d}{d x} (cos^{3} (5 x + 1))

Solution

- 15 cos^{2} (5 x + 1) sin (5 x + 1)

Solution steps

\frac{d}{d x} (cos^{3} (5 x + 1))

Apply the chain rule:

3 (cos (5 x + 1))^{2} \frac{d}{d x} (cos (5 x + 1))

= 3 (cos (5 x + 1))^{2} \frac{d}{d x} (cos (5 x + 1))

\frac{d}{d x} (cos (5 x + 1)) = - sin (5 x + 1) \cdot 5

= 3 (cos (5 x + 1))^{2} (- sin (5 x + 1) \cdot 5)

Simplify

= - 15 cos^{2} (5 x + 1) sin (5 x + 1)

Popular Examples

y^{''}+4y=-6,y(pi/8)=-12,y^'(pi/8)=2

y^{^{''}} + 4 y = - 6, y (\frac{π}{8}) = - 12, y^{^{'}} (\frac{π}{8}) = 2

derivative of (x-1e^{-x})

\frac{d}{d x} ((x - 1) e^{- x})

derivative of e^{3xy}

\frac{d}{d x} (e^{3 x y})

limit as h approaches 0 of ((f(h)(4+h)-f(4)))/h

h \to 0 lim (\frac{( f ( h ) ( 4 + h ) - f ( 4 ) )}{h})

(\partial)/(\partial x)(e^{-x}cos(y))

\frac{\partial}{\partial x} (e^{- x} cos (y))

Frequently Asked Questions (FAQ)

What is the derivative of cos^3(5x+1) ?
The derivative of cos^3(5x+1) is -15cos^2(5x+1)sin(5x+1)
What is the first derivative of cos^3(5x+1) ?
The first derivative of cos^3(5x+1) is -15cos^2(5x+1)sin(5x+1)