Math virtual assistant

About Snapxam Calculators Topics Go Premium
ENGESP
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

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

Derive the function x^2cos(4x-5) with respect to x

Answer

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

Step-by-step explanation

Problem

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

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

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

Unlock this step-by-step solution!

Answer

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

Main topic:

Differential calculus

Used formulas:

4. See formulas

Time to solve it:

0.25 seconds