how do you find the derivative of ((x)^7x)?

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how do you find the derivative of ((x)^7x)?

2006-11-03 07:34:41 · 3 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics

3 answers

I | AUG is not correct. You cannot differentiate power functions by the exponent rule. (Even doing that, she made an error.) The implicit differentiation done by Greg G is correct, or you can use the functional power rule:

d(ƒ^g)/dx = (ƒ^g)*[(dƒ/dx)*(g/ƒ) + (dg/dx)*lnƒ]

2006-11-03 08:10:06 · answer #1 · answered by gp4rts 7 · 1⤊ 0⤋

The derivative is 7x * x^6x * 7 = 49x^(6x+1)

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2006-11-03 07:52:28 · answer #2 · answered by I ♥ AUG 6 · 0⤊ 1⤋

y=x^(7x)
ln(y)= 7xln(x)
(1/y)dy/dx=7(ln(x)+1)
dy/dx=7y(ln(x)+1)
dy/dx= 7(x^(7x))(ln(x)+1)

2006-11-03 07:38:24 · answer #3 · answered by Greg G 5 · 3⤊ 0⤋