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Finding derivative of Inverse trigonometric functions
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Derivative of cot-1 x (cot inverse x) You are here
Derivative of sec-1 x (Sec inverse x)
Derivative of cosec-1 x (Cosec inverse x)
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Finding derivative of Inverse trigonometric functions
Last updated at March 23, 2023 by Teachoo
Derivative of γπππγ^(βπ) π π (π₯)=γπππ‘γ^(β1) π₯ Let π= γπππγ^(βπ) π cotβ‘γπ¦=π₯γ π=ππ¨πβ‘γπ γ Differentiating both sides π€.π.π‘.π₯ ππ₯/ππ₯ = (π (cotβ‘π¦ ))/ππ₯ 1 = (π (cotβ‘π¦ ))/ππ₯ Γ ππ¦/ππ¦ 1 = (π (cotβ‘π¦ ))/ππ¦ Γ ππ¦/ππ₯ 1 = βππ¨γπ¬ππγ^π π . ππ¦/ππ₯ 1 = β(π +πππππ) ππ¦/ππ₯ ππ¦/ππ₯ = (β1)/(1 + γππ¨πγ^πβ‘π ) Putting πππ‘β‘π¦ = π₯ ππ¦/ππ₯ = (β1)/(π^π + π) Hence (π (γππ¨πγ^(βπ)β‘γπ)γ)/π π = (βπ)/(π^π + π) (π΄π γ πππ ππγ^2β‘γπ¦= γ1+γβ‘γπππ‘γ^2β‘π¦ γ) As π¦ = γπππ‘γ^(β1) π₯ So, πππβ‘π = π