Find the Derivative - d/dx y = square root of 3-5x

Problem

d()/d(x)√(,3−5*x)

Solution

1. Identify the function as a composition of functions, where the outer function is the square root u(1/2) and the inner function is u=3−5*x

2. Apply the power rule and the chain rule to differentiate the outer function with respect to the inner function.

d(√(,u))/d(u)=1/2*u(−1/2)

3. Differentiate the inner function 3 - 5xw*i*t*h*r*e*s(p)*e*c*t*t*o$.

d(3−5*x)/d(x)=−5

4. Multiply the derivative of the outer function by the derivative of the inner function according to the chain rule.

d(y)/d(x)=1/2*(3−5*x)(−1/2)⋅(−5)

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

d(y)/d(x)=−5/(2√(,3−5*x))

Final Answer

d(√(,3−5*x))/d(x)=−5/(2√(,3−5*x))

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