The expression -√x^1.8 can be simplified further.
Using the power rule of exponents, we have:
-√x^1.8 = -√(x^(9/5))
Taking the square root of x^(9/5), we can simplify it as:
-√(x^(9/5)) = -x^(9/10)
So the simplified expression is -x^(9/10).
-√x^1.8
5 answers
more simplify
Apologies for the confusion. To simplify the expression -√x^1.8 further, we can rewrite it as:
-√x^1.8 = -x^(1.8/2)
Now, let's simplify the exponent by dividing it by 2:
-√x^1.8 = -x^0.9
Therefore, the simplified expression is -x^0.9.
-√x^1.8 = -x^(1.8/2)
Now, let's simplify the exponent by dividing it by 2:
-√x^1.8 = -x^0.9
Therefore, the simplified expression is -x^0.9.
answer by dx/dy rule
To find the derivative of -√x^1.8 using the power rule, we need to differentiate each part separately.
Let's start by differentiating -√x. Using the chain rule, we have:
d/dx (-√x) = -1/2 * (x^(-1/2)) = -1/(2√x)
Next, let's differentiate x^1.8. Using the power rule, we have:
d/dx (x^1.8) = 1.8 * (x^(1.8 - 1)) = 1.8x^0.8
Now, we can apply the product rule to find the derivative of the entire expression:
d/dx (-√x^1.8) = d/dx (-√x) * x^1.8 + (-√x) * d/dx (x^1.8)
= -1/(2√x) * x^1.8 + (-√x) * 1.8x^0.8
= -x^1.8/(2√x) + (-√x) * 1.8x^0.8
Simplifying further, we have:
= -x^1.8/(2√x) - 1.8√x * x^0.8
Therefore, the derivative of -√x^1.8 with respect to x is -x^1.8/(2√x) - 1.8√x * x^0.8.
Let's start by differentiating -√x. Using the chain rule, we have:
d/dx (-√x) = -1/2 * (x^(-1/2)) = -1/(2√x)
Next, let's differentiate x^1.8. Using the power rule, we have:
d/dx (x^1.8) = 1.8 * (x^(1.8 - 1)) = 1.8x^0.8
Now, we can apply the product rule to find the derivative of the entire expression:
d/dx (-√x^1.8) = d/dx (-√x) * x^1.8 + (-√x) * d/dx (x^1.8)
= -1/(2√x) * x^1.8 + (-√x) * 1.8x^0.8
= -x^1.8/(2√x) + (-√x) * 1.8x^0.8
Simplifying further, we have:
= -x^1.8/(2√x) - 1.8√x * x^0.8
Therefore, the derivative of -√x^1.8 with respect to x is -x^1.8/(2√x) - 1.8√x * x^0.8.