What is the derivative of sec(x(x-tan(x))) ?

The derivative of sec(x(x-tan(x))) is xsec(x)tan(x)-2tan^2(x)sec(x)

What is the first derivative of sec(x(x-tan(x))) ?

The first derivative of sec(x(x-tan(x))) is xsec(x)tan(x)-2tan^2(x)sec(x)

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

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

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = sec (x), g = x - tan (x)

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

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

\frac{d}{d x} (x - tan (x)) = - tan^{2} (x)

= sec (x) tan (x) (x - tan (x)) + (- tan^{2} (x)) sec (x)

Simplify

sec (x) tan (x) (x - tan (x)) + (- tan^{2} (x)) sec (x) : x sec (x) tan (x) - 2 tan^{2} (x) sec (x)

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

y^{^{''}} + 4 y^{^{'}} + 4 y = e^{- 2 x}

x = 6 y^{2}, x = 4 + 2 y^{2}

f (x) = x (x^{6} - 1), at x = 1

\int e^{x} \cdot cos (3 x) d x

\int \frac{6 x ^{2} - 15 x + 22}{( x + 3 ) ( x ^{2} + 2 ) ^{2}} d x

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