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# differentiating watch

1. How do you differentiate y = sinh^(n-1) x cosh x

to get

dy/dx = (n-1)sinh^(n-2) x + nsinh^n x

???
2. Note that the derivative of (sinhx)^(n-1) is (n-1)coshx.(sinhx)^(n-2). So, using the product rule, you get:
dy/dx = (n-1)coshx.(sinhx)^(n-2).coshx + sinhx.(sinhx)^(n-1)
= (n-1) (sinhx)^(n-2) (coshx)^2 + (sinhx)^n
= (n-1) (sinhx)^(n-2) [1 + (sinhx)^2] + (sinhx)^n
= (n-1) (sinhx)^(n-2) + (n-1) (sinhx)^n + (sinhx)^n
= (n-1) (sinhx)^(n-2) + n (sinhx)^n
3. (Original post by lesser weevil)
How do you differentiate y = sinh^(n-1) x cosh x

to get

dy/dx = (n-1)sinh^(n-2) x + nsinh^n x

???
well, just use d(uv) = udv + vdu
where u = sinhx^(n-1) -> du = (n-1)sinhx^(n-2).coshx
v = coshx -> dv = sinhx
and cosh²x - sinh²x = 1
4. thanks mate.

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