Find the Derivative - d/dx 15 root of 7x+5

Problem

d()/d(x)√(15,7*x+5)

Solution

1. Rewrite the radical expression using a fractional exponent to make it easier to differentiate.

√(15,7*x+5)=(7*x+5)1/15

2. Apply the chain rule, which states that the derivative of ƒ*(g(x)) is ƒ′*(g(x))⋅g(x)′

d()/d(x)*(7*x+5)1/15=1/15*(7*x+5)(1/15−1)⋅d(7*x+5)/d(x)

3. Subtract the exponents and calculate the derivative of the inner function 7*x+5

1/15−1=−14/15

d(7*x+5)/d(x)=7

4. Substitute these values back into the derivative expression.

1/15*(7*x+5)(−14/15)⋅7

5. Simplify the expression by multiplying the constants and moving the negative exponent to the denominator.

7/(15*(7*x+5)14/15)

Final Answer

d(√(15,7*x+5))/d(x)=7/(15*(7*x+5)14/15)

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