Question

Compute The following derivatives. Please explain step by step

(x^3+e^2x)'=

Answer 1

@mathslover

Answer 2

know the derivative of x^n ?

Answer 3

can you show me step by step @hartnn

Answer 4

First we split the derivative,

\(\Large (x^3 + e^{2x})' = (x^3)' + (e^{2x})'\)

Answer 5

then since we know \((x^n)' = n x^{n-1}\)
\(\Large (x^3)' = 3x^{3-1} = 3x^2\)

Answer 6

and \((e^x)'=e^x\)
but since we have 2x as exponent, we need to use chain rule.
\(\large (e^{2x})' = e^{2x} (2x)' = 2e^{2x}\)

so, your derivative would finally be
\(\Large 3x^22e^{2x}\)

Answer 7

i mean
\(\Large 3x^2+2e^{2x}\)

Answer 8

Good job @hartnn

Answer 9

ok can you tell me why do you split the two above 1ST?

Answer 10

50_cent msg hartnn so he can continue to assist you...I'm sorry but I don't know this stuff >.>

Answer 11

because we can split it up,
\((A+B)' = A'+B'\)

its the rule in differentiation.

sum of differentials, is the differentials of sum

Answer 12

can you help me to understand how to use d/dt ((5-2t)(t+1))?

Answer 13

multiply them out first
(5-2t)(t+1)
foil

Answer 14

Or still use the product rule.