(t^4)-(7^t) derivative?

Question

Explain please.

Answer 1

Greetings,

Let me rewrite 7^t as e^(tln7) which has a derivative of

ln7*e^(tln7)

so the derivative we seek is

4t^3 - ln7*7^t

Regards

Answer 2

This function can be split into 2 parts:

The derivative of the first part, t^4, is just using the power rule:
4*t^3

The next part, 7^t is a little trickier, but just use the exponent rules:

d/dx[a^x] = ln(a)*a^x, so the derivative of this would be ln(7)*7^t. Now put the 2 together:

4*t^3 - ln(7)*7^t

Answer 3

its'=4* t ^3 - t*7^(t-1)

Answer 4

The first term is a power rule derivitive, or
d(t^4)/dt = 4t^3
The second term is an exponential rule derivitive
d(7^t)/dt = (7^t)ln7

Answer 5

well t^4 is easy to do, a variable to a constant, constants to a variable are much harder. i think you have to use logs, or natural logs(ln x) to write the 7^t portion correctly.

though i so wish it could just be (t)(7^(t-1)) and leave it at that lol.

Answer 6

4t^3 - 7^t (ln7)
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Ideas: (7^t)' = [e^(t ln7)]' = e^(t ln7) (ln7) = 7^t(ln7)