What is the derivative of f(x)=cot^{tan(x)}(x) ?

The derivative of f(x)=cot^{tan(x)}(x) is cot^{tan(x)}(x)(sec^2(x)ln(cot(x))-sec^2(x))

What is the first derivative of f(x)=cot^{tan(x)}(x) ?

The first derivative of f(x)=cot^{tan(x)}(x) is cot^{tan(x)}(x)(sec^2(x)ln(cot(x))-sec^2(x))

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derivative of

f (x) = cot^{t a n (x)} (x)

cot^{t a n (x)} (x) (sec^{2} (x) ln (cot (x)) - sec^{2} (x))

Solution steps

\frac{d}{d x} (cot^{t a n (x)} (x))

Apply exponent rule:

a^{b} = e^{b l n (a)}

cot^{t a n (x)} (x) = e^{t a n (x) l n (c o t (x))}

= \frac{d}{d x} (e^{t a n (x) l n (c o t (x))})

Apply the chain rule:

e^{t a n (x) l n (c o t (x))} \frac{d}{d x} (tan (x) ln (cot (x)))

= e^{t a n (x) l n (c o t (x))} \frac{d}{d x} (tan (x) ln (cot (x)))

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

= e^{t a n (x) l n (c o t (x))} (sec^{2} (x) ln (cot (x)) - sec^{2} (x))

e^{t a n (x) l n (c o t (x))} = cot^{t a n (x)} (x)

= cot^{t a n (x)} (x) (sec^{2} (x) ln (cot (x)) - sec^{2} (x))

y = \frac{x}{1 + x ^{2}}

x^{3} sin (x)

y^{^{'}} - 0.5 y = - 430, y (0) = 840

\int_{\frac{1}{2}}^{1} x cos (π x) d x

\int_{0}^{5} \frac{1}{9 + 4 x ^{2}} d x

What is the derivative of f(x)=cot^{tan(x)}(x) ?
The derivative of f(x)=cot^{tan(x)}(x) is cot^{tan(x)}(x)(sec^2(x)ln(cot(x))-sec^2(x))
What is the first derivative of f(x)=cot^{tan(x)}(x) ?
The first derivative of f(x)=cot^{tan(x)}(x) is cot^{tan(x)}(x)(sec^2(x)ln(cot(x))-sec^2(x))