How do you find the derivative of # -2- (1/(x^2)) + (4/(x^4))#? Calculus Basic Differentiation Rules Quotient Rule 1 Answer Lucio Falabella Jan 14, 2016 #f'(x)=2(x^2-8)/x^5# Explanation: Remembering that: #d/dxsum_(i=1)^nk_i*f_i(x)=d/dx[k_1f_1(x)+k_2f_2(x)+...+k_nf_n(x)]=# #=k_isum_(i=1)^nd/dxf_i(x)=k_1f_1'(x)+k_2f_2'(x)+...+k_nf_n'(x)# And #d/dx(g(x)/(h(x)))=(h'(x)*g(x)-g'(x)*h(x))/(g^2(x))# given: #f(x)=-2-1/x^2+4/x^4# #:.f'(x)=0-((0*x^2-1*2x)/x^4)+4*((0*x^4-4x^3)/x^8)=# #=-(-2cancel(x)/(x^(cancel(4)^3)))+4*(-4cancel(x^3)/x^(cancel(8)^5))=# #=2/x^3-16/x^5=2/x^3(1-8/x^2)=2/x^3(x^2-8)/x^2=2(x^2-8)/x^5# Answer link Related questions What is the Quotient Rule for derivatives? How do I use the quotient rule to find the derivative? How do you prove the quotient rule? How do you use the quotient rule to differentiate #y=(2x^4-3x)/(4x-1)#? How do you use the quotient rule to differentiate #y=cos(x)/ln(x)#? How do you use the quotient rule to find the derivative of #y=tan(x)# ? How do you use the quotient rule to find the derivative of #y=x/(x^2+1)# ? How do you use the quotient rule to find the derivative of #y=(e^x+1)/(e^x-1)# ? How do you use the quotient rule to find the derivative of #y=(x-sqrt(x))/(x^(1/3))# ? How do you use the quotient rule to find the derivative of #y=x/(3+e^x)# ? See all questions in Quotient Rule Impact of this question 1427 views around the world You can reuse this answer Creative Commons License