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Popular Calculus >

derivative of cos^2(3x+1-sin^2(3x+1))

Solution

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

Solution

- sin (2 (1 + 3 x)) \cdot 6

Solution steps

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

Simplify

cos^{2} (3 x + 1) - sin^{2} (3 x + 1) : cos (2 (1 + 3 x))

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

Apply the chain rule:

- sin (2 (1 + 3 x)) \frac{d}{d x} (2 (1 + 3 x))

= - sin (2 (1 + 3 x)) \frac{d}{d x} (2 (1 + 3 x))

\frac{d}{d x} (2 (1 + 3 x)) = 6

= - sin (2 (1 + 3 x)) \cdot 6

Graph

Popular Examples

integral of sqrt(1+sin(x))

\int 1 + sin (x) d x

derivative of f(x)=sqrt(5+4e^{3x)}

d er i v a t i v e f (x) = 5 + 4 e^{3 x}

y^{''}+16y^'+64y=0,y(0)=-3,y^'(0)=28

y^{^{''}} + 16 y^{^{'}} + 64 y = 0, y (0) = - 3, y^{^{'}} (0) = 28

integral from 0 to 8 of sqrt(1+81/4 x)

\int_{0}^{8} 1 + \frac{81}{4} x d x

derivative of 4x^2-6x+2

d er i v a t i v e 4 x^{2} - 6 x + 2

Frequently Asked Questions (FAQ)

What is the derivative of cos^2(3x+1-sin^2(3x+1)) ?
The derivative of cos^2(3x+1-sin^2(3x+1)) is -sin(2(1+3x))*6
What is the first derivative of cos^2(3x+1-sin^2(3x+1)) ?
The first derivative of cos^2(3x+1-sin^2(3x+1)) is -sin(2(1+3x))*6