## Class 11 RS Aggarwal Chapter-28 Differentiation Solutions

## FAQs on RS Aggarwal Class 11 Solutions Chapter-28 Differentiation

**1. Differentiate sin(3x+5)**

Let say,

y = sin (3x+5)

dy/dx = d[sin(3x+5)]/dx

From the chain rule, we can rewrite it as ,

= cos (3x+5) d(3x+5)/dx

= cos (3x+5) [3]

y’ = 3 cos (3x+5)

d[sin(3x+5)]/dx = 3 cos (3x+5)

**2. Differentiate 10x ^{2} concerning x.**

Let us assume that,

y = 10x^{2}

y’ = d(10x^{2})/dx

y’ = 2.10.x = 20x

Therefore, d(10x^{2})/dx = 20 x

Hence, it is solved.

**3. Differentiate y = tan θ (sin θ + cos θ)**

It is given that,

y = tan θ (sin θ + cos θ)

u = tan θ ==> u' = sec^{2} θ

v = sin θ + cos θ ==> v' = cos θ - sin θ

By substituting the values,

dy/dx = tan θ (cos θ - sin θ) + (sin θ + cos θ) (sec^{2}θ)

= tan θ cos θ - tan θ sin θ + sin θ sec^{2}θ + cos θ sec^{2}θ

= sin θ - (sin^{2} θ/cos θ) + (sin θ/cos^{2}θ) + (1/cos θ)

= sin θ - (sin^{2} θ/cos θ) + (tan θ sec θ) + (1/cos θ)

= sin θ - ((1 - sin^{2}θ)/cos θ) + (tan θ sec θ)

= sin θ - (cos^{2}θ/cos θ) + (tan θ sec θ)

Therefore, we will get,

dy/dx = sin θ - cos θ + tan θ sec θ

**4. How do I differentiate between integration and differentiation?**

Differentiation and Integration are the two major branches of calculus. The distinction between differentiation and integration, on the other hand, is difficult to grasp. Many students and even academics are baffled by the distinction. The distinction between differentiation and integration is that differentiation is used to determine instant rates of change and curve slope. Differentiation is used to identify the instant rates of change from one point to another and to calculate the gradient of a curve. Whereas integration is used to determine the area under curves. As you can see, in terms of mathematical significance, differentiation and integration are opposed.

**5. Is differentiation used in physics as well?**

When we need to find the rate of something in physics, we employ differentiation. Simply put, it's for calculating the rate, and the slope of the tangent at a particular point on a curve, and so on. As a result, whenever you need to determine a rate of change, you should employ differentiation. Things like speeds and accelerations, slopes and curves, and so on are all part of differentiation. These are Rates of Change, which are defined on a local level.