How do you differentiate y=10^x with respect to x?

Question

?? Thanks..

Answer 1

y=10^x = e^(x ln 10)
Applying the chain rule:
dy/dx = e^(x ln 10) * ln 10 = 10^x ln 10
And in general:
d(a^x)/dx = a^x ln a

Answer 2

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Do you know how to differentiate? Multiply the term by its power and then reduce the power by one. 1. y' = 2x + 1.5x^-1/4 - 4x^-5 - 2x^-5/4 To differentiate e, multiply the term by the coefficient of x in the power 2. y' = 3e^x + 3x^-1/2 3. y' = -15x^-5/2 + 4 For products, use the product rule: y' = u(dv/dx) + v(du/dx) 4. y' = xe^x + e^x = (x+1)e^x 5 and 6 are more difficult. It's a while since I did this stuff and I can't really remember how to solve the last two so don't take my word on these. Wait for someone else to respond and back them up before you go writing them down. I think 5 should be: 5. y' = 5x(x^2 - 5)^3/2 and if my memory serves me correctly, 6 will be: 6. y' = (4x^-1/3)e^6x^2/3 Sorry I can't be more sure about the last two. Get yourself a calculus textbook and go over the rules of differentiation. It's a lot easier seeing it written out in proper mathematical form rather than ridiculous expressions like these.

Answer 3

Derivative Of 10 X

Answer 4

It's always helpful for me to rewrite these in terms of e^x if I forget the formulas:

10^x = e^(ln(10^x)) = e^(x*ln10)

The derivative of this with respect to x is ln(10)*e^(x*ln10) = ln(10)*e^(ln(10^x)) = ln(10) * 10^x

In general, the derivative of a^x is ln(a) * a^x where a>0

Answer 5

answer is 10^x *logx
y=10^x
take log on both sides
logy=x*log10
now differentiate
1/y dy/dx=log10
dy/dx=ylog10
dy/dx=10^xlog10 [as y=10^x]

NOTE: all log all are natural log ,that is ln

Answer 6

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How do you differentiate y=10^x with respect to x?
?? Thanks..

Answer 7

ln(y) = ln(10^x) = x*ln(10)

1/y * dy/dx = ln(10)

dy/dx = y*ln(10) = (10^x)*ln(10)