What is the function derivative?

What is the derivative of this function?

• Answer:

    f(t) = 9 ^ ( t^4)   or   f(t) = (9^t) ^ 4 edit: f(t) = 9 ^ ( t^4) ... u =  t^4 f(t) = 9 ^ u In your book it should say: d { a^u } ⁄ dt = (a^u) • ln[a] • (du ⁄ dt) ... where: "a" is a constant. f  '  (t) = (9 ^ u) • ln[9] • (du ⁄ dt) ... equation 1 f  '  (t) = (9 ^ u) • ln[9] • ( 4 t³ ) f  '  (t) = 4 ln[9] • t³ •  [9 ^ ( t^4) ] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~... ... or I could have used logarithmic differentiation: y = 9 ^ u ... natural log both sides ln[y] = u • ln[9] ... differentiate: dy ⁄ dt = ý ý ⁄ y = ln[9] • (du ⁄ dt) ý = y • ln[9] • (du ⁄ dt) ... substitute for "y" ý = (9 ^ u) • ln[9] • (du ⁄ dt) ... same as equation 1