# Step-by-step Solution

Go!
1
2
3
4
5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

## Step-by-step explanation

Problem to solve:

$\frac{d}{dx}\left(5\left(\sin\left(x\right)+\cos\left(x\right)\right)\left(\sin\left(x\right)-\cos\left(x\right)\right)\right)$

Learn how to solve product rule of differentiation problems step by step online.

$\frac{d}{dx}\left(5\left(\sin\left(x\right)^2-\cos\left(x\right)^2\right)\right)$

Learn how to solve product rule of differentiation problems step by step online. Find the derivative using the product rule (d/dx)(5(sin(x)+cos(x))*(sin(x)-cos(x))). Solve the product of difference of squares 5\left(\sin\left(x\right)+\cos\left(x\right)\right)\left(\sin\left(x\right)-\cos\left(x\right)\right). Solve the product 5\left(\sin\left(x\right)^2-\cos\left(x\right)^2\right). The derivative of a sum of two functions is the sum of the derivatives of each function. The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function.

$20\sin\left(x\right)\cos\left(x\right)$

### Problem Analysis

$\frac{d}{dx}\left(5\left(\sin\left(x\right)+\cos\left(x\right)\right)\left(\sin\left(x\right)-\cos\left(x\right)\right)\right)$

### Main topic:

Product rule of differentiation

~ 1.25 seconds