Verified answer

Differentiate each term, using power rule d/dx xⁿ = nx^(n - 1). Remember that the derivative of the constant is 0!

f'(t) = -4t + 3

f'(x) = 1

I hope this helps!

Remember that the Power Rule of Derivatives states that the derivative of a*x^n with respect to x equals: a*n*(x^(n-1)). Also, since a constant has a degree of x^0, the derivative of any constant is 0 by the Power Rule.

So, using the rule, f'(t)=(-2*2)t^(2-1) + (3*1)t^(1-1) - (0*6)x^(0-1).

Evaluating: f'(t)= -4t+3

f'(x)= 1*x^(1-1) + 0 = 1

Therefore:

the derivative of f(t) is -4t+3

the derivative of f(x) is 1.

f(t) = -2t^2+3t-6

=> f'(t) = -2 * 2 * t + 3

=> f'(t) = -4 * t + 3

f(x)= x+1

=> f'(x) = 1