What is the derivative of sec^2(x/a+csc^2(x/a)) ?

The derivative of sec^2(x/a+csc^2(x/a)) is (2sec^2(x/a)tan(x/a)-2csc^2(x/a)cot(x/a))/a

What is the first derivative of sec^2(x/a+csc^2(x/a)) ?

The first derivative of sec^2(x/a+csc^2(x/a)) is (2sec^2(x/a)tan(x/a)-2csc^2(x/a)cot(x/a))/a

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

\frac{2 sec ^{2} ( \frac{x}{a} ) tan ( \frac{x}{a} ) - 2 csc ^{2} ( \frac{x}{a} ) cot ( \frac{x}{a} )}{a}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

\frac{d}{d x} (csc^{2} (\frac{x}{a})) = - \frac{2 csc ^{2} ( \frac{x}{a} ) cot ( \frac{x}{a} )}{a}

= \frac{2 sec ^{2} ( \frac{x}{a} ) tan ( \frac{x}{a} )}{a} - \frac{2 csc ^{2} ( \frac{x}{a} ) cot ( \frac{x}{a} )}{a}

Apply rule

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{2 sec ^{2} ( \frac{x}{a} ) tan ( \frac{x}{a} ) - 2 csc ^{2} ( \frac{x}{a} ) cot ( \frac{x}{a} )}{a}

f (x) = x^{2} - 6, (2, - 2)

x \to - \infty lim (2. 3^{x})

2 y^{^{''}} + 35 y = 0

x \to 2 lim (\frac{x ^{2}}{x ^{2} + 1})

\int e^{- in x} d x

What is the derivative of sec^2(x/a+csc^2(x/a)) ?
The derivative of sec^2(x/a+csc^2(x/a)) is (2sec^2(x/a)tan(x/a)-2csc^2(x/a)cot(x/a))/a
What is the first derivative of sec^2(x/a+csc^2(x/a)) ?
The first derivative of sec^2(x/a+csc^2(x/a)) is (2sec^2(x/a)tan(x/a)-2csc^2(x/a)cot(x/a))/a