t(x)=((x+4)^0.1-5x)^-5.1
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find derivarive
The given function is t(x) = ((x+4)^0.1 - 5x)^-5.1.
To understand this function, let's break it down step by step:
Step 1: The expression inside the outermost parentheses is (x+4)^0.1 - 5x. This means we need to evaluate the term (x+4)^0.1 and subtract 5x from it.
Step 2: The expression (x+4)^0.1 represents the 0.1 power of (x+4). To calculate this, we need to raise (x+4) to the power of 0.1.
Step 3: The next step is to subtract 5x from the result of step 2.
Step 4: The resulting expression from step 3 is then raised to the power of -5.1.
Let's see an example of evaluating this function for a specific value of x:
Example: Let's say we want to calculate t(2).
Step 1: Start by substituting x = 2 into the expression inside the outermost parentheses: (2+4)^0.1 - 5(2)
=> (6)^0.1 - 10
Step 2: Calculate the 0.1 power of 6:
=> 1.56508458 - 10
Step 3: Subtract 10 from the result of step 2:
=> -8.43491542
Step 4: Finally, raise the result of step 3 to the power of -5.1:
=> (-8.43491542)^-5.1
Thus, t(2) = (-8.43491542)^-5.1.
Note: You can substitute any value you want for x and follow these steps to evaluate the function at that specific value.