find the derivative of f(x)=2x^2+5

d/dx of  2 x^2  = (2) 2x^(2-1) = 4x

d/dx of a constant is '0'                     so f'(x) = 4x

Find the derivative of the following via implicit differentiation:
d/dx(f(x)) = d/dx(5+2 x^2)
The derivative of f(x) is f'(x):
f'(x) = d/dx(5+2 x^2)
Differentiate the sum term by term and factor out constants:
f'(x) = d/dx(5)+2 d/dx(x^2)
The derivative of 5 is zero:
f'(x) = 2 (d/dx(x^2))+0
Simplify the expression:
f'(x) = 2 (d/dx(x^2))
Use the power rule, d/dx(x^n) = n x^(n-1), where n = 2: d/dx(x^2) = 2 x:
f'(x) = 2 2 x
Simplify the expression:
f'(x) = 4 x
Expand the left hand side:
Answer: |  f'(x) = 4x