# Step-by-step Solution

## Find the derivative using the product rule (d/dx)(x^2cos(4*x-5))

Go
1
2
3
4
5
6
7
8
9
0
x
y
(◻)
◻/◻
2

e
π
ln
log
lim
d/dx
d/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

### Videos

$2x\cos\left(4x-5\right)-4x^2\sin\left(4x-5\right)$

## Step-by-step explanation

Problem to solve:

$\frac{d}{dx}\left(x^2\cos\left(4x-5\right)\right)$
1

Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=x^2$ and $g=\cos\left(4x-5\right)$

$\frac{d}{dx}\left(x^2\right)\cos\left(4x-5\right)+x^2\frac{d}{dx}\left(\cos\left(4x-5\right)\right)$
2

The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$, then $f'(x) = nx^{n-1}$

$2x\cos\left(4x-5\right)+x^2\frac{d}{dx}\left(\cos\left(4x-5\right)\right)$

$2x\cos\left(4x-5\right)-4x^2\sin\left(4x-5\right)$
$\frac{d}{dx}\left(x^2\cos\left(4x-5\right)\right)$

### Main topic:

Differential calculus

~ 0.35 seconds