Differentiate w.r.t. x the function(3x2 – 9x + 5)9

Q1 of 147 Page 191

Differentiate w.r.t. x the function
(3x² – 9x + 5)⁹

Let y = (3x² – 9x + 5)⁹

If u = v(w(x))

Then using chain rule

∴ Differentiating y w.r.t. x using chain rule

= 9(3x² – 9x + 5)⁸×(6x – 9)

=9(3x² – 9x + 5)⁸ × 3(2x – 3)

=27(3x² – 9x + 5)⁸ (2x – 3)

∴

Verify Mean Value Theorem, if f (x) = x³ – 5x² – 3x in the interval [a, b], where a = 1 and b = 3. Find all c ∈ (1, 3) for which f′(c) = 0.

Examine the applicability of Mean Value Theorem for all three functions given in the above exercise 2.

Differentiate w.r.t. x the function

sin³ x + cos⁶ x

Differentiate w.r.t. x the function

(5x)^{3cos 2x}