Find the Derivative - d/d@VAR f(x) = square root of 1-4x

Problem

d()/d(x)√(,1−4*x)

Solution

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

√(,1−4*x)=(1−4*x)(1/2)

2. Apply the power rule to the outer function, which is the exponent 1/2

d(1−4*x)/d(x)=1/2*(1−4*x)(−1/2)⋅d(1−4*x)/d(x)

3. Apply the chain rule by finding the derivative of the inner function 1−4*x

d(1−4*x)/d(x)=−4

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

1/2*(1−4*x)(−1/2)⋅−4=−2*(1−4*x)(−1/2)

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

−2*(1−4*x)(−1/2)=(−2)/√(,1−4*x)

Final Answer

d(√(,1−4*x))/d(x)=−2/√(,1−4*x)

Want more problems? Check here!