Calculus: Chain Rule

Easy

Medium

Difficult

Q1) Find the derivative of \( \left( x ^{2} + 1\right) ^{-4} \)
Q1) Find the derivative of \( \left( 3 x ^{7} + 10\right) ^{\frac{3}{7} } \)
Q1) Find the derivative of \( \ln \left( x ^{2} + 1\right) \)
Q2) Find the derivative of \( \left( 4 x ^{3} + 3 x ^{2}\right) ^{-7} \)
Q2) Find the derivative of \( \left( 6 x ^{7} + 13\right) ^{\frac{6}{7} } \)
Q2) Find the derivative of \( \cos \left( x ^{2} + 1\right) \)
Q3) Find the derivative of \( 7776 x ^{5} + 45360 x ^{4} + 105840 x ^{3} + 123480 x ^{2} + 72030 x + 16807 \)
Q3) Find the derivative of \( \left( 5 x ^{9} + 14\right) ^{\frac{5}{9} } \)
Q3) Find the derivative of \( \exp \left( 3 x ^{2} + 2\right) \)
Q4) Find the derivative of \( 4096 x ^{18} + 18432 x ^{17} + 34560 x ^{16} + 34560 x ^{15} + 19440 x ^{14} + 5832 x ^{13} + 729 x ^{12} \)
Q4) Find the derivative of \( \sqrt{4 x ^{8} + 12} \)
Q4) Find the derivative of \( \ln \left( x ^{2} + 1\right) \)
Q5) Find the derivative of \( \left( 4 x ^{3} + 3 x ^{2}\right) ^{-3} \)
Q5) Find the derivative of \( \left( 4 x ^{9} + 13\right) ^{\frac{4}{9} } \)
Q5) Find the derivative of \( \cos \left( 4 x ^{3} + 25\right) \)