Product rule:


Power rule:

The exponential function is its own derivative:

Assuming the base of
is
, its derivative is

But if you mean a logarithm of arbitrary base
, we have



So we end up with


Answer with Step-by-step explanation:
Let us assume the 2 consecutive natural numbers are 'n' and 'n+1'
Thus the product of the 2 numbers is given by

We know that the sum of 'n' consecutive natural numbers starting from 1 is

Thus from equation 'i' we can write

As we know that any number multiplied by 2 is even thus we conclude that the product of 2 consecutive numbers is even.
Answer:
90 deg
Step-by-step explanation:
Recall that for a rhombus, the diagonals always intersect at right angles.
Hence angle PXM is 90 deg
Answer:
5kg
Step-by-step explanation:
Here the given force is 2500N and
acceleration is 500m/s²
Now,
F = ma
m = F/a = 2500/500 = 5kg
Thus, The mass is 5kg
<u>-The</u><u>UnknownScientist</u>
Answer:
ΔABC ~ ΔDEF
Step-by-step explanation:
If the given triangles ΔABC and ΔDEF are similar,
Their corresponding sides will be proportional.

By substituting the measures of the given sides,

2 = 2 = 2
Since, corresponding sides of both the triangles are proportional, both the triangles will be similar.
ΔABC ~ ΔDEF