Find d y d x for the following y = x 7 2 .

Given function is y = x 7 2 We have to find d y d x for the given function. Differentiation is a process, where we find the instantaneous rate of change in function based on one of its variables. Now, y = x 7 2 Differentiate with respect to the x . d y d x = 7 2 x 7 2 - 1 d y d x = 7 2 x 5 2

Find d y d x for the following y = x – 3

given y = x – 3 we have to find differentiation of y with respect to x d d x ( x - 3 ) = - 3 x - 3 - 1 ∴ d d x x n = n . x n - 1 d y d x = - 3 x - 4

Find d y d x for the following y = x

Given function is y = x Differentiating both sides of the given function with respect to x we have, d y d x = d d x x d y d x = 1 × x 1 - 1 d y d x = 1 × x 0 d y d x = 1 × 1 d y d x = 1 Hence, d y d x = 1

Find d y d x for the following y = x 5 + x 3 + 4 x 1 2 + 7

It is given that y = x 5 + x 3 + 4 x 1 2 + 7 Differentiate y with respect to x We get d y d x = 5 x 5 - 1 + 3 x 3 - 1 + 4 × 1 2 x 1 2 - 1 + 0 d y d x = 5 x 4 + 3 x 2 + 2 x - 1 2 + 0 We can write above equation as d y d x = 5 x 4 + 3 x 2 + 2 x

Find d y d x for the following y = 5 x 4 + 6 x 3 2 + 9 x

Given function is y = 5 x 4 + 6 x 3 2 + 9 x Differentiating both sides of the given function with respect to x we have, d y d x = d d x 5 x 4 + 6 x 3 2 + 9 x d y d x = d d x 5 x 4 + d d x 6 x 3 2 + d d x 9 x d y d x = 5 d d x x 4 + 6 d d x x 3 2 + 9 d d x x d y d x = 5 × 4 x 3 + 6 × 3 2 × x 3 2 - 1 + 9 × 1 d y d x = 20 x 3 + 9 x 1 2 + 9

Find d y d x for the following y = a x 2 + b x + c .

Given: y = a x 2 + b x + c Differentiate y w.r.t. x , we get ⇒ d y d x = 2 a x 2 - 1 + b x 1 - 1 + 0 ⇒ d y d x = 2 a x + b

Find d y d x for the following y = 3 x 5 – 3 x – 1 x

Given function is y = 3 x 5 – 3 x – 1 x We have to find a d y d x for a given function. Differentiation is a process, where we find the instantaneous rate of change in function based on one of its variables. Now, y = 3 x 5 – 3 x – 1 x Differentiating both sides of the given function with respect to x we have, d y d x = d d x 3 x 5 – 3 x – 1 x d y d x = d d x 3 x 5 - d d x 3 x - d d x 1 x d y d x = 3 d d x x 5 - 3 d d x x - d d x x - 1 d y d x = 3 × 5 x 4 - 3 × 1 - - 1 × x - 2 ∵ d d x x n = n x n - 1 , n ∈ R d y d x = 15 x 4 - 3 + 1 x 2