Q: Differentiate the function y = 2x^7 + x^2 - 3/x^5 + x^1/4 - 54e^x +16
Can someone explain how to solve this?
Can someone explain how to solve this?
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d/dx(2*x^7) = 7*x^(7 - 1) = 7*x^6
d/dx( - 3/x^5) = - 3*x^(- 5) = ( - 5)*( - 3)*x^( - 5 - 1) = 15*x^( - 6) = 15*(1/x^6)
d/dx( - 54*e^x) = - 54*e^x*ln(e) = - 54*e^x
d/dx(16) = d/dx(16*x^0) = 0*16*(x^(0 - 1) = 0
d/dx(2x^7 + x^2 - 3/x^5 + x^1/4 - 54e^x +16) = 14*x^6 +2*x + 15*(1/x^6) + (1/4)*(1/x^(3/4) - 54*e^x
d/dx( - 3/x^5) = - 3*x^(- 5) = ( - 5)*( - 3)*x^( - 5 - 1) = 15*x^( - 6) = 15*(1/x^6)
d/dx( - 54*e^x) = - 54*e^x*ln(e) = - 54*e^x
d/dx(16) = d/dx(16*x^0) = 0*16*(x^(0 - 1) = 0
d/dx(2x^7 + x^2 - 3/x^5 + x^1/4 - 54e^x +16) = 14*x^6 +2*x + 15*(1/x^6) + (1/4)*(1/x^(3/4) - 54*e^x
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The answer is
14x^6+2x + 15/x^6 + 1/4 -54e^x
Use the power rule for exponents derivitive of x^n = nx^n-1
Quotient rule for 3/(x^5) would be [(3)'(x^5) - 3(x^5)' ]/ (x^5)^2 which is 15/x^6
derivative of e^x is just e^x
Derivative of a constant is 0
14x^6+2x + 15/x^6 + 1/4 -54e^x
Use the power rule for exponents derivitive of x^n = nx^n-1
Quotient rule for 3/(x^5) would be [(3)'(x^5) - 3(x^5)' ]/ (x^5)^2 which is 15/x^6
derivative of e^x is just e^x
Derivative of a constant is 0