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Popular >

derivative of tan(sec(cos(x)))

Solution

\frac{d}{d x} (tan (sec (cos (x))))

Solution

- sec^{2} (sec (cos (x))) sec (cos (x)) tan (cos (x)) sin (x)

Solution steps

\frac{d}{d x} (tan (sec (cos (x))))

Apply the chain rule:

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

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

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

= sec^{2} (sec (cos (x))) (- sec (cos (x)) tan (cos (x)) sin (x))

Simplify

= - sec^{2} (sec (cos (x))) sec (cos (x)) tan (cos (x)) sin (x)

Graph

Popular Examples

slope of y^4-4y^2=x^4-9x^2,(-3,2)slope

y^{4} - 4 y^{2} = x^{4} - 9 x^{2}, (- 3, 2)

derivative of (1/(y^2)-3/(y^4))(y+5y^3)derivative of

(\frac{1}{y ^{2}} - \frac{3}{y ^{4}}) (y + 5 y^{3})

(dy)/(dx)=(e^{x-y})

\frac{d y}{d x} = (e^{x - y})

integral from 2 to x^3 of t^4

\int_{2}^{x^{3}} t^{4} d t

y^{''}-2y^'-3y=3e^2t

y^{^{''}} - 2 y^{^{'}} - 3 y = 3 e^{2} t

Frequently Asked Questions (FAQ)

What is the derivative of tan(sec(cos(x))) ?
The derivative of tan(sec(cos(x))) is -sec^2(sec(cos(x)))sec(cos(x))tan(cos(x))sin(x)
What is the first derivative of tan(sec(cos(x))) ?
The first derivative of tan(sec(cos(x))) is -sec^2(sec(cos(x)))sec(cos(x))tan(cos(x))sin(x)