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Popular Calculus >

derivative of (sin(2x+1)/(cos(-1-2x)))

Solution

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

Solution

sec^{2} (1 + 2 x) \cdot 2

Solution steps

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

Simplify

\frac{sin ( 2 x + 1 )}{cos ( - 1 - 2 x )} : tan (1 + 2 x)

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

Apply the chain rule:

sec^{2} (1 + 2 x) \frac{d}{d x} (1 + 2 x)

= sec^{2} (1 + 2 x) \frac{d}{d x} (1 + 2 x)

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

= sec^{2} (1 + 2 x) \cdot 2

Graph

Popular Examples

(d^2)/(dx^2)(cos(6x))

\frac{d ^{2}}{d x ^{2}} (cos (6 x))

limit as x approaches-1 of x(0)

x \to - 1 lim (x (0))

limit as x approaches 0 of 3f(x)(x^2)

x \to 0 lim (3 f (x) (x^{2}))

integral of cos(sqrt(3x))

\int cos (3 x) d x

limit as x approaches 0+of xln(2x)

x \to 0 + lim (x ln (2 x))

Frequently Asked Questions (FAQ)

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