What is the derivative of (tan^2(x)/(tan(x^2))) ?

The derivative of (tan^2(x)/(tan(x^2))) is 2sec^2(x)tan(x)cot(x^2)-2xcsc^2(x^2)tan^2(x)

What is the first derivative of (tan^2(x)/(tan(x^2))) ?

The first derivative of (tan^2(x)/(tan(x^2))) is 2sec^2(x)tan(x)cot(x^2)-2xcsc^2(x^2)tan^2(x)

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

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

Solution steps

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

Simplify

\frac{tan ^{2} ( x )}{tan ( x ^{2} )} : tan^{2} (x) cot (x^{2})

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

Apply the Product Rule:

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

f = tan^{2} (x), g = cot (x^{2})

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

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

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

= 2 tan (x) sec^{2} (x) cot (x^{2}) + (- csc^{2} (x^{2}) \cdot 2 x) tan^{2} (x)

Simplify

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

x \frac{d y}{d x} = e^{7 y + x}

n = 1 \sum \infty 5 (- \frac{1}{6})^{5 n}

f (x) = \frac{2 x ^{2} - x - 1}{2 x + 2}

x \to 0 + lim (x^{20 x})

\frac{d}{d x} (7 x^{4} cot (x))

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