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

Problem

d()/d(x)*(x2−35)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 u7 with respect to u where u=x2−35

d(y)/d(x)=7*(x2−35)6⋅d(x2−35)/d(x)

3. Differentiate the inner function x2−35 with respect to x

d(x2−35)/d(x)=2*x

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

d(y)/d(x)=7*(x2−35)6⋅2*x

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

d(y)/d(x)=14*x*(x2−35)6

Final Answer

d()/d(x)*(x2−35)7=14*x*(x2−35)6

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