𝑑/𝑑𝑥 [log {𝑒 ^𝑥( 𝑥−2 / 𝑥+2 ) ^3/4 }] is equal to

Derivative of 2√cot ( 𝑥 ²) with respect to 𝑥 is

Derivative of √𝑒 ^√𝑥 with respect to 𝑥 is

If 𝑥 = 4𝑡, 𝑦 = 4/𝑡 , 𝑑𝑦 / 𝑑𝑥 is equal to

If 𝑥 = 𝛼(cos θ + θ sin θ) and 𝑦 = 𝛼(sin θ + θ cos θ), then 𝑑𝑦/𝑑𝑥 is equal to

Derivative of √𝑡𝑎𝑛∛𝑥  with respect to 𝑥 is

If 𝑥 = 𝛼 𝑠𝑒𝑐³ θ and 𝑦 = 𝛼 𝑡𝑎𝑛³ θ then the value of 𝑑𝑦/𝑑𝑥 at θ = π /3 is

Derivative of log[log(log 𝑥 ⁵)] with respect to 𝑥 is

If 𝑥 = 𝑡 + 1 /𝑡 and 𝑦 = 𝑡 − 1/ 𝑡 , then 𝑑𝑦/𝑑𝑥 is equal to

If 𝑥 = 1+log 𝑡 /𝑡 ² and 𝑦 = 3+2 log 𝑡 /𝑡 ² , then 𝑑𝑦/𝑑𝑥 is equal

The value of 𝑑𝑦/𝑑𝑥 [(𝑡𝑎𝑛² 2𝑥−𝑡𝑎𝑛² 𝑥 / 1−𝑡𝑎𝑛² 2𝑥 𝑡𝑎𝑛² 𝑥) cot 3𝑥] is

If 𝑦 = 𝑙𝑜𝑔^𝑛 𝑥, where 𝑙𝑜𝑔^𝑛 means log log log………(repeated n times), then 𝑥 𝑙𝑜𝑔 𝑥 𝑙𝑜𝑔² 𝑥 𝑙𝑜𝑔³𝑥 … … … = 𝑙𝑜𝑔^𝑛−1 𝑥 𝑙𝑜𝑔 ^𝑛𝑥 𝑑𝑦/𝑑𝑥 is equal to

If 𝑓(𝑥) = √1 + 𝑐𝑜𝑠²(𝑥²) , then the value of 𝑓′ (√𝜋/2) is

If 𝑓(𝑥) = (𝑙𝑜𝑔_{cot 𝑥} tan 𝑥)(𝑙𝑜𝑔_{cot 𝑥} cot 𝑥)⁻¹ + 𝑡𝑎𝑛⁻¹ 4𝑥 / 4−𝑥², then 𝑓′(𝑥) is equal to

If 𝑓(𝑥) = 𝑙𝑜𝑔_𝑥(𝑙𝑜𝑔_𝑥 𝑥) then 𝑓′(𝑥) at 𝑥 = 𝑒 is equal to

Let 𝑓(𝑥) = 𝑒^𝑥, 𝑔(𝑥) = 𝑠𝑖𝑛⁻¹𝑥 and ℎ(𝑥) = 𝑓[𝑔(𝑥)], then ℎ′(𝑥) / ℎ(𝑥)is equal to

Let 𝑓(𝑥) = sin 𝑥 , 𝑔(𝑥) = 𝑥² and ℎ(𝑥) = 𝑙𝑜𝑔_𝑒𝑥. If 𝐹(𝑥) = (ℎ𝑜𝑔𝑜𝑓)(𝑥), then 𝐹′′(𝑥) is equal to

If 𝑥𝑦 + 𝑦² = tan 𝑥 + 𝑦, 𝑡ℎ𝑒𝑛 𝑑𝑦/𝑑𝑥 is equal to

If 𝑠𝑖𝑛²𝑥 + 𝑐𝑜𝑠²𝑦 = 1, then 𝑑𝑦/𝑑𝑥 is equal to

If 𝑥√1 + 𝑦 + 𝑦√1 + 𝑥 = 0 for −1 < 𝑥 < 1, then 𝑑𝑦/𝑑𝑥 is

Q.If (𝑥 − 𝑎) ² + (𝑦 − 𝑏) ² = 𝑐 ² , for some c > 0, then [1+( 𝑑𝑦 /𝑑𝑥) ² ] ^3/2 / 𝑑²𝑦 / 𝑑𝑥² is

If cos 𝑦 = 𝑥 cos (𝑎 + 𝑦), with cos 𝛼 ≠ 1 ,then 𝑑𝑦/𝑑𝑥 is equal to

If x sin(𝑎 + 𝑦) + sin 𝛼 cos (𝑎 + 𝑦) = 0, then 𝑑𝑦/𝑑𝑥 is equal to

If 𝑦 = √sin 𝑥 + 𝑦, then 𝑑𝑦/𝑑𝑥 is equal to

Differential coefficient of 𝑡𝑎𝑛⁻¹ ( √1+𝑥 ²−1 / 𝑥 ) with respect to 𝑡𝑎𝑛⁻¹𝑥, when 𝑥 ≠ 0, is

Derivative of cos 𝑥. cos 2𝑥. cos 3𝑥 with respect to 𝑥 is

If 𝑦 ² = 𝑥 ^𝑦, then 𝑑𝑦/𝑑𝑥 is equal to

If 𝑥𝑦 = 𝑒 ^{(𝑥−𝑦)} , then 𝑑𝑦/𝑑𝑥 is equal to

If 𝑓(𝑥) = (1 + 𝑥)(1 + 𝑥 ²)(1 + 𝑥 ⁴)(1 + 𝑥 ⁸ ) , then the value of 𝑓′(𝑥)

Derivative of (log 𝑥) ^{log 𝑥} with respect to 𝑥 is

If 𝑦 ^𝑥 = 𝑒 ^𝑦−𝑥 , then 𝑑𝑦/𝑑𝑥 is equal to

If 𝑥 = 𝑒^𝑥/𝑦, then 𝑑𝑦/𝑑𝑥 is equal to

If 𝑦 = (cos 𝑥)^{(cos 𝑥)cos 𝑥………..∞}, then 𝑑𝑦/𝑑𝑥 is equal to

If 𝑥^𝑚. 𝑥^𝑛 = (𝑥 + 𝑦)^𝑚+𝑛, then which of the option is correct

If 𝑥 = 𝑒𝑥𝑝 {𝑡𝑎𝑛⁻¹(𝑦−𝑥²/𝑥²)} , then 𝑑𝑦/𝑑𝑥 is equal to

If cos 𝑥/2 cos 𝑥/2² cos 𝑥/2³ … … … … cos 𝑥/2^𝑛 = 𝑓(𝑥), then 1/2 tan 𝑥/2+1/2² tan 𝑥/2² + ⋯ +1/2² tan 𝑥/2^𝑛 is equal to

If 𝑦 = 𝑠𝑖𝑛⁻¹(1−𝑥²/1+𝑥²), 0 < 𝑥 < 1, then 𝑑𝑦/𝑑𝑥 is equal to

If 𝑦 = 𝑐𝑜𝑠⁻¹ (2𝑥/1+𝑥²), −1 < 𝑥 < 1, then 𝑑𝑦/𝑑𝑥 is equal to

Differential coefficient of 𝑐𝑜𝑡−1[√1+sin 𝑥 +√1−sin 𝑥 / √1+sin 𝑥 −√1−sin 𝑥], 0 < 𝑥 <𝜋/2 is

If 𝑦 = 𝑠𝑖𝑛⁻¹𝑥 + 𝑠𝑖𝑛⁻¹√1 − 𝑥², −1 ≤ 𝑥 ≤ 1, then 𝑑𝑦/𝑑𝑥 is

Differentiate 𝑐𝑜𝑠⁻¹[sin 𝑥+cos 𝑥 / √2] with respect to 𝑥 is

Differentiate 𝑡𝑎𝑛⁻¹[a cos 𝑥− b sin 𝑥 / b cos 𝑥+ a sin 𝑥] , −𝜋2< 𝑥 <𝜋/2 and 𝑎/𝑏 tan 𝑥 > −1 , then 𝑑𝑦/𝑑𝑥 is

If √1 − 𝑥² + √1 − 𝑦² = 𝑎(𝑥 − 𝑦), then 𝑑𝑦/𝑑𝑥 is equal to

Derivative of 𝑠𝑖𝑛⁻¹[1/√𝑥+1] with respect to 𝑥 is

If y = t𝑎𝑛⁻¹(sec 𝑥 − tan 𝑥) ,then 𝑑𝑦/𝑑𝑥 is equal to

If 𝑠𝑖𝑛⁻¹𝑥 + 𝑠𝑖𝑛⁻¹𝑦 =𝜋/2, then 𝑑𝑦/𝑑𝑥 is equal to

𝑑/𝑑𝑥 [𝑠𝑖𝑛²𝑐𝑜𝑡⁻¹ {√1−𝑥/1+𝑥}] is equal to

𝑑/𝑑𝑥[𝑠𝑖𝑛⁻¹(𝑥√1 − 𝑥 − √𝑥 √1 − 𝑥²] is equal to

If 𝑦 = 𝑡𝑎𝑛⁻¹ [log(𝑒/𝑥² ) / log(𝑒𝑥²)] + 𝑡𝑎𝑛⁻¹ [3+2 𝑙𝑜𝑔 𝑥 / 1−6 𝑙𝑜𝑔 𝑥 ] , then 𝑑²𝑦 / 𝑑𝑥² is equal to

If 𝑦 = [𝑡𝑎𝑛⁻¹ 1/1+𝑥+𝑥² + 𝑡𝑎𝑛⁻¹ 1/𝑥²+3𝑥+3+ 𝑡𝑎𝑛⁻¹ 1/𝑥²+5𝑥+7+ ⋯ + 𝑢𝑝𝑡𝑜 𝑛 𝑡𝑒𝑟𝑚𝑠], then 𝑦′(0) is equal to