Find the Derivative - d/dx y=(x^2-35)^7

Problem

d()/d(x)*(x^2−35)^7

Solution

1. Identify the outer function and the inner function to apply the Chain Rule.

2. Apply the Chain Rule by differentiating the outer function u^7 with respect to u where u=x^2−35

d(y)/d(x)=7*(x^2−35)^6⋅d(x^2−35)/d(x)

3. Differentiate the inner function x^2−35 with respect to x

d(x^2−35)/d(x)=2*x

4. Multiply the results together to find the final derivative.

d(y)/d(x)=7*(x^2−35)^6⋅2*x

5. Simplify the expression by multiplying the constants and variables outside the parentheses.

d(y)/d(x)=14*x*(x^2−35)^6

Final Answer

d()/d(x)*(x^2−35)^7=14*x*(x^2−35)^6

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