Find the Derivative - d/dx y=5xarcsin(x)

Problem

d()/d(x)*5*x*arcsin(x)

Solution

1. Identify the rule needed for the derivative. Since the expression is a product of two functions, 5*x and arcsin(x) use the product rule: (d(u)*v)/d(x)=ud(v)/d(x)+vd(u)/d(x)

2. Assign the functions for the product rule. Let u=5*x and v=arcsin(x)

3. Differentiate each part individually. The derivative of u is (d(5)*x)/d(x)=5 The derivative of v is d(arcsin(x))/d(x)=1/√(,1−x2)

4. Apply the product rule formula by substituting the functions and their derivatives.

(d(5)*x*arcsin(x))/d(x)=(5*x)1/√(,1−x2)+arcsin(x)*(5)

5. Simplify the expression by combining terms.

(d(5)*x*arcsin(x))/d(x)=(5*x)/√(,1−x2)+5*arcsin(x)

Final Answer

(d(5)*x*arcsin(x))/d(x)=(5*x)/√(,1−x2)+5*arcsin(x)

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