Find d y d x for the following: y = x 4

Given, y = x 4 We have to find d y d x for the given equation. Differentiation is a process, where we find the instantaneous rate of change in function based on one of its variables. We know that, If y = a x n , then d y d x = n × a × x n - 1 Now, y = x 4 and d y d x = 4 × x 4 - 1 = 4 x 3 Hence, d y d x = 4 x 3 for y = x 4 .

Find d y d x for the following: y = x 6

Given, y = x 6 We have to find d y d x for the given equation. Differentiation is a process, where we find the instantaneous rate of change in function based on one of its variables. We know that, If y = a x n , then d y d x = n × a × x n - 1 Now, y = x 6 and d y d x = 6 × x 6 - 1 = 6 x 5 Hence, d y d x = 6 x 5 for y = x 6 .

Find d y d x for the following: y = x 9

Given, y = x 9 We have to find d y d x for the given equation. Differentiation is a process, where we find the instantaneous rate of change in function based on its variable. We know that, If y = a x n , then d y d x = n × a × x n - 1 Now, y = x 9 and d y d x = 9 × x 9 - 1 = 9 x 8 Hence, d y d x = 9 x 8 for y = x 9 .

Find d y d x for the following: y = 4 x 3

Given, y = 4 x 3 We have to find d y d x for the given equation. Differentiation is a process, where we find the instantaneous rate of change in function based on one of its variables. We know that, If y = a x n , then d y d x = n × a × x n - 1 Now, y = 4 x 3 and d y d x = 4 × 3 × x 3 - 1 = 12 x 2 Hence, d y d x = 12 x 2 for y = 4 x 3 .

E M B I B E

Cambridge IGCSE® Mathematics Core and Extended Coursebook Second Edition>Chapter 18 - Curved Graphs>Exercise 18.10>Q 1

MEDIUM

Upper Secondary: IGCSE

IMPORTANT

Earn 100

The gradient of the graph at the point $(1.5, 2.25)$ is $3$ . Write down the coordinates of the point at which the gradient is $- 3$ .

Important Questions on Curved Graphs

MEDIUM

Upper Secondary: IGCSE

IMPORTANT

Cambridge IGCSE® Mathematics Core and Extended Coursebook Second Edition>Chapter 18 - Curved Graphs>Exercise 18.10>Q 2

The graph shows how the population of a village has changed since $1930$ . Find the gradient of the graph at the point $(1950, 170)$ .

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MEDIUM

Upper Secondary: IGCSE

IMPORTANT

Cambridge IGCSE® Mathematics Core and Extended Coursebook Second Edition>Chapter 18 - Curved Graphs>Exercise 18.10>Q 2

The graph shows how the population of a village has changed since $1930$ . Find the gradient of the graph the point $(1950, 170)$ . What does this gradient represent.

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