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What is the derivative of y equals the quantity 2x plus 5 raised to 8 plus 4x all raised to3?
I am interpreting this as:
Find the derivative of:
y=((2x+5)8+4x)3
To find the derivative (y'), the chain rule must be applied. The "outermost" function of this compound function is t3 (t being an arbitrary quantity). The derivative of t3 is 3t2 * dt, where "dt" is the derivative of the quantity "t". Applying this, we arrive at a working definition of y':
y' = 3((2x+5)8+4x)2(derivative of (2x+5)8+4x)
The derivative of (2x+5)8+4x is found using basic derivative definitions and the chain rule again:
8(2x+5)7(2)+4 = 16(2x+5)7+4
So now we can write y' again:
y'= 3((2x+5)8+4x)2(16(2x+5)7+4) = 48((2x+5)8+4x)2((2x+5)7+4)
This can be further simplified, but this is an arduous process. If you need further simplification, feel free to contact me via private message.
What else can I help you with?
What is the derivative of F of x equals 7x squared plus 5?
14x
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How do you derivative x plus y - 1 equals ln x2 plus y2?
There are several steps involved in how one can solve the derivative x plus y - 1 equals x2 plus y2. The final answer to this math problem is y'(x) = (1-2 x)/(2 y-1).
What is the derivative of y equals aex plus be2x plus ce3x with respect to x?
if y=aex+be2x+ce3x then its derivative dy/dx or y' is: y'=aex+2be2x+3ce3x
What is the first and second derivative of R equals q2 plus 3qa plus a2?
Rprime= 2q + 2a + 3 Rdoubleprime= 4
Derivative of x equals 5x plus 5x?
x = 10x, so derivative = 10
What is the derivative of F of x equals 7x squared plus 5?
14x
Find the derivative y equals sq rt 7 plus 99 plus pie?
y is a sum of constants and so is itself a constant. Its derivative is, therefore, zero.
3rd derivative of y equals mx plus b?
The first derivative is m and the second is 0 so the third is also 0.
What is the derivative of x2 plus 6 divided by 2?
Following the correct order of operations: derivative of x^2 + 6/2 = derivative of x^2 +3, which equals 2x
How do you derivative x plus y - 1 equals ln x2 plus y2?
There are several steps involved in how one can solve the derivative x plus y - 1 equals x2 plus y2. The final answer to this math problem is y'(x) = (1-2 x)/(2 y-1).
What is the derivative of y equals aex plus be2x plus ce3x with respect to x?
if y=aex+be2x+ce3x then its derivative dy/dx or y' is: y'=aex+2be2x+3ce3x
What is Y double-prime plus y equals 0?
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What is the answer to the problem X cubed plus six x squared plus three x plus one divided by x minus two?
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What is the first and second derivative of R equals q2 plus 3qa plus a2?
Rprime= 2q + 2a + 3 Rdoubleprime= 4
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x = 3.5
Calcuate the quantity of x and it's maximum error if x equals 6a plus 4b where a equals 40 tolerance is plus or minus 2 and b equals 20 plus or minus 2?
320 tolerance +/- 20 ? Did I get it right?
