What is the derivative of sec(x-1/(x^3)+5) ?

The derivative of sec(x-1/(x^3)+5) is 3/(x^4)+sec(x)tan(x)

What is the first derivative of sec(x-1/(x^3)+5) ?

The first derivative of sec(x-1/(x^3)+5) is 3/(x^4)+sec(x)tan(x)

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

\frac{3}{x ^{4}} + sec (x) tan (x)

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (sec (x)) - \frac{d}{d x} (\frac{1}{x ^{3}}) + \frac{d}{d x} (5)

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

\frac{d}{d x} (\frac{1}{x ^{3}}) = - \frac{3}{x ^{4}}

\frac{d}{d x} (5) = 0

= sec (x) tan (x) - (- \frac{3}{x ^{4}}) + 0

Simplify

= \frac{3}{x ^{4}} + sec (x) tan (x)

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

8 y^{^{''}} - 8 y^{^{'}} + 4 y = 0

\frac{d y}{d x} = 9 - \frac{3 y}{250}

Y (x) = e^{4 x + 3}

\frac{d}{d y} (y^{2} - 1)

What is the derivative of sec(x-1/(x^3)+5) ?
The derivative of sec(x-1/(x^3)+5) is 3/(x^4)+sec(x)tan(x)
What is the first derivative of sec(x-1/(x^3)+5) ?
The first derivative of sec(x-1/(x^3)+5) is 3/(x^4)+sec(x)tan(x)