Find the derivatives of the following functions with respect to corresponding independent variables: Draw the function f'(x) if f(x) = 2x2 – 5x + 3

Find the derivatives of the following functions with respect to corresponding independent variables:

Draw the function f'(x) if f(x) = 2x² – 5x + 3

Chart

Diagram

f(x) = 2x2 – 5x + 3

f'(x) = 4x – 5 which is a linear function

(i.e.) y = 4x – 5

x	0	1	2	3
y	– 5	– 1	3	7

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Chapter 10: Differential Calculus - Differentiability and Methods of Differentiation - Exercise 10.2 [Page 160]

Chapter 10 Differential Calculus - Differentiability and Methods of Differentiation
Exercise 10.2 | Q 20 | Page 160

Find the derivatives of the following functions with respect to corresponding independent variables:

g(t) = t³ cos t

Find the derivatives of the following functions with respect to corresponding independent variables:

y = `(tanx - 1)/secx`

Find the derivatives of the following functions with respect to corresponding independent variables:

y = tan θ (sin θ + cos θ)

Differentiate the following:
y = (x² + 4x + 6)⁵

Differentiate the following:
F(x) = (x³ + 4x)⁷

Differentiate the following:

f(t) = `root(3)(1 + tan "t")`

Differentiate the following:
y = cos (a³ + x³)

Differentiate the following:
y = (2x – 5)⁴ (8x² – 5)^–3

Differentiate the following:

f(x) = `x/sqrt(7 - 3x)`

Differentiate the following:

y = `5^((-1)/x)`

Find the derivatives of the following:

`sqrt(x^2 + y^2) = tan^-1 (y/x)`

Find the derivatives of the following:

`tan^-1 = ((6x)/(1 - 9x^2))`

Find the derivatives of the following:

x = `(1 - "t"^2)/(1 + "t"^2)`, y = `(2"t")/(1 + "t"^2)`

Find the derivatives of the following:

Find the derivative with `tan^-1 ((sinx)/(1 + cos x))` with respect to `tan^-1 ((cosx)/(1 + sinx))`

Find the derivatives of the following:

If y = e^tan–1x, show that (1 + x²)y” + (2x – 1)y’ = 0