Question

Differentiate the following functions with respect to x (a) x^(4) + 3x^(2) -2x (b) x^(2) cos x (c) (6x +7)^(4) (d) e^(x) x^(5) (e) ((1 + x))/(e^(x))

Answer 1

Answer:

(a) 4x³ + 6x - 2

(b) -2 x sin(x)

(c) Using Binomial Theorem,

(6x +7)^4 = (6x)⁴ + (4) (6x)³ (7) + (6) (6x)² (7)² + (4) (6x) (7)³ + (7)⁴

d/dx = (6⁴) (4) x³ + (28) (6³) (3) x² + (6³) (7²) x + (24) (7³)*

Please evaluate by powers.

(d) Using Quotient Rule,

[(1) × e^x - (e^x) (1-x) ] / [ ( e^x)² ]

= e^x - e^x + x e^x / e^2x

= x / e²

PLEASE MARK AS BRAINLIEST.

Answer 2

The answer to the questions are given below in the attachment.

The first differentiation problem requires the method of binomial differention.

The second requires the rule of multiplication in differention.

The third is also a case for binomial ans successive differentiation.

The fourth is a case for multiplicative differentiation

The fifth is a case for the division rule in differentiation.