Find dy/dx y=(10x^3+7)^(3/2)

Problem

d()/d(x)*(10*x3+7)(3/2)

Solution

1. Identify the outer function and the inner function to apply the Chain Rule. The outer function is u(3/2) and the inner function is u=10*x3+7

2. Apply the Power Rule to the outer function by bringing the exponent down and subtracting one from the exponent.

d(y)/d(x)=3/2*(10*x3+7)(1/2)⋅d(10*x3+7)/d(x)

3. Differentiate the inner function 10*x3+7 with respect to x

d(10*x3+7)/d(x)=30*x2

4. Multiply the results of the outer and inner derivatives together.

d(y)/d(x)=3/2*(10*x3+7)(1/2)⋅30*x2

5. Simplify the expression by multiplying the constants.

d(y)/d(x)=45*x2*(10*x3+7)(1/2)

Final Answer

d(y)/d(x)=45*x2√(,10*x3+7)

Want more problems? Check here!