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

Problem

d()/d(x)√(,5−3*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=5−3*x

2. Rewrite the square root using a fractional exponent to make it easier to differentiate.

y=(5−3*x)(1/2)

3. Apply the chain rule, which states that the derivative is the derivative of the outer function evaluated at the inner function, multiplied by the derivative of the inner function.

d(y)/d(x)=1/2*(5−3*x)(−1/2)⋅d(5−3*x)/d(x)

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

d(5−3*x)/d(x)=−3

5. Substitute the inner derivative back into the expression.

d(y)/d(x)=1/2*(5−3*x)(−1/2)⋅(−3)

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

d(y)/d(x)=−3/(2√(,5−3*x))

Final Answer

d(√(,5−3*x))/d(x)=−3/(2√(,5−3*x))

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