Find the derivative of f(x)=x2sinh−1(2x)?

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Answer 1 · 2018-03-31T21:24:24

#f'(x)=2(sinh(x)+xcosh(x)-1)#

I am assuming that we have:

#f(x)=2x*sinh(x)-2x#

Some rules to remember:

Product rule:
#d/dx[f(x)*g(x)]=f'(x)*g(x)+f(x)*g'(x)#

#d/dx[sinh(x)]=cosh(x)#

#d/dx[x^n]=nx^(n-1)# if #n# is a constant.

#=>f'(x)=d/dx[2x]*sinh(x)+2x*d/dx[sinh(x)]-d/dx[2x]#

#=>f'(x)=2*sinh(x)+2x*cosh(x)-2# Factor

#=>f'(x)=2(sinh(x)+xcosh(x)-1)#