How do you find the derivative of #y = ((x^5)/6) + (1/(10x^3)) #?

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How do you find the derivative of #y = ((x^5)/6) + (1/(10x^3)) #?

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Answer 1 · 2016-03-26T02:06:41

#f'(x) = 5/6x^4 - 3/(10x^4)#

Explanation:

Given: #f(x)=y=color(red)((x^5)/6) + color(blue)(1/(10x^3)) #
Required: #f'(x)=(dy)/dx#?
Definition and principles:
#color(red)((dx^n)/dx=nx^(n-1))# and
#color(blue)(d/dx(1/n^k)=-kx^(-k-1))#

Solution strategy: Apply the power rules above:
#(dy)/dx= color(red)(5/6x^4) + 1/10color(blue)((-3/x^4 ))#

#f'(x) = 5/6x^4 - 3/(10x^4)#

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How do you find the derivative of #y = ((x^5)/6) + (1/(10x^3)) #?

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