Find the derivative of x 5 cos x sinx
Asked by admin @ in Math viewed by 369 People
Find the derivative of x5-cosx/sinx
Answered by admin @
d/dx {(x⁵ - cosx) / sinx}
= - x⁵ cosecx cotx + 5x⁴ cosecx - cosec²x
Step-by-step explanation:
Let y = (x⁵ - cosx) / sinx
= (x⁵ / sinx) - (cosx / sinx)
= x⁵ cosecx - cotx
Now differentiating both sides w.r. to x, we get
dy / dx = d/dx (x⁵ cosecx - cotx)
= d/dx (x⁵ cosecx) - d/dx (cotx)
= x⁵ d/dx (cosecx) + cosecx d/dx (x⁵) + d/dx (cotx)
= x⁵ (- cosecx cotx) + cosecx (5x⁴) + (- cosec²x)
= - x⁵ cosecx cotx + 5x⁴ cosecx - cosec²x
Rules:
• d/dx (xⁿ) = n xⁿ⁻¹, where n is rational
• d/dx (cosecx) = - cosecx cotx
• d/dx (cotx) = - cosec²x
Related question:
Differentiate Sin inverse of 2 X upon oneplus x square with respect to Cos inverse of 1 - x square upon oneplus x square. - brainly.in/question/3911961
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