4x to the sixth can be expanded to (4x * 4x * 4x)(4x * 4x * 4x) or (4x to the third)(4x to the third) the square root of the above would be 4x to the third
square root of 4x is 2 times square root of x, so answer is square root of x times 3 since it is 2 square roots of x plus one of them
Derivative with respect to 'x' of (5x)1/2 = (1/2) (5x)-1/2 (5) = 2.5/sqrt(5x)
x2 + 4x = 41
0
I believe you are asking: What is the derivative (d/dx) of (4x+25)^0.5 If this is indeed the case, the derivative d((4x+25)^0.5)/dx = 0.5*(4x+25)^-0.5*4 = 2(4x+25)^-0.5 That is, 2 times the quantity (4x+25) to the negative 1/2 power.
y=(8x).5 + (4x).5 = (2+2sqrt(2))x.5 y'=(1 + sqrt(2))/sqrt(x)
4x to the sixth can be expanded to (4x * 4x * 4x)(4x * 4x * 4x) or (4x to the third)(4x to the third) the square root of the above would be 4x to the third
We use the property of square roots that says the square root of (ab)=square root (a) multiplied by square root of b So square root (4x)=square root (4) mutiplies by square root of x =2(square root (x)) 2sqrt(x)
square root of 4x is 2 times square root of x, so answer is square root of x times 3 since it is 2 square roots of x plus one of them
Derivative of 4x is 4.
The square root of x = x to the power of a half
the derivative is 0. the derivative of a constant is always 0.
The derivative of sqrt(2) is zero.
If you square an expression and then take the square root, the squaring and the square root cancel one another, EXCEPT that the sign will be positive. Thus, if you square 16x, and then take the square root, the answer can be 16x or -16x, depending on whether "x" is positive or negative. Or if you only square x, and then take the square root of the entire expression, it would be 4x or -4x (once again, depending on whether "x" is positive or negative).
Use the formula for the derivative of a power. The square root of (x-5) is the same as (x-5)1/2.
The square root of 4x^2 is solved by first doing the square root of 4. This is plus or minus two - because -2 x -2=4. The square root of x^2 is x. So the answers are 2x or -2x. If your question was (4x)^2, then the answer would be 4x.