Question

differentian of tan (√9x+3 )3
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Answer 1

Answer:

1. Differentiate x5 with respect to x.

Solution: Given, y = x5

On differentiating w.r.t we get;

dy/dx = d(x5)/dx

y’ = 5x5-1 = 5x4

Therefore, d(x5)/dx = 5x4

2. Differentiate 10x2 with respect to x.

Solution: y = 10x2

y’ = d(10x2)/dx

y’ = 2.10.x = 20x

Therefore, d(10x2)/dx = 20 x

3. Differentiate 20x-4 + 9.

Solution: y = 20x-4 + 9

y’ = d(20x-4 + 9)/dx

y’ = d(20x-4)/dx + d(9)/dx

y’ = -4.20.x-4-1+0

y’ = -80x-5

Therefore, d(20x-4 + 9)/dx = -80x-5

4. Differentiate ln(10).

Solution: y = ln(x)

Differentiate y w.r.t x

dy/dx = d(ln(10))/dx

y’ = 1/10

Therefore, d(ln 10)/dx = 1/10

Rules of Differentiation:

Sum and Difference : f'(x)=u'(x)±v'(x)

Product rule: f′(x)=u′(x)×v(x)+u(x)×v′(x)

Quotient Rule : f′(x)=u′(x)×v(x)−u(x)×v′(x)(v(x))2

Chain Rule: dy/dx = dy/du × du/dx

Step-by-step explanation:

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