Find the Derivative - d/d@VAR f(x) = square root of 2-6x

Problem

d()/d(x)√(,2−6*x)

Solution

1. Rewrite the square root as a power to prepare for differentiation.

√(,2−6*x)=(2−6*x)(1/2)

2. Apply the power rule and the chain rule by differentiating the outer function while keeping the inner function the same.

d(2−6*x)/d(x)=1/2*(2−6*x)(−1/2)⋅d(2−6*x)/d(x)

3. Differentiate the inner function 2 - 6xw*i*t*h*r*e*s(p)*e*c*t*t*o$.

d(2−6*x)/d(x)=−6

4. Multiply the results of the power rule and the derivative of the inner function.

1/2*(2−6*x)(−1/2)⋅(−6)=−3*(2−6*x)(−1/2)

5. Simplify the expression by moving the negative exponent to the denominator and converting it back to radical form.

−3*(2−6*x)(−1/2)=(−3)/√(,2−6*x)

Final Answer

d(√(,2−6*x))/d(x)=(−3)/√(,2−6*x)

Want more problems? Check here!