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Find the derivative of $x\cos\left(x^2-1\right)$

Step-by-step Solution

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Final answer to the problem

$\cos\left(x^2-1\right)+x\left(-2x\right)\sin\left(x^2-1\right)$
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Step-by-step Solution

How should I solve this problem?

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  • Find the derivative using the definition
  • Find the derivative using the product rule
  • Find the derivative using the quotient rule
  • Find the derivative using logarithmic differentiation
  • Find the derivative
  • Integrate by partial fractions
  • Product of Binomials with Common Term
  • FOIL Method
  • Integrate by substitution
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1

Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=

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

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

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Learn how to solve problems step by step online. Find the derivative of xcos(x^2-1). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=. The derivative of the linear function is equal to 1. The derivative of the cosine of a function is equal to minus the sine of the function times the derivative of the function, in other words, if f(x) = \cos(x), then f'(x) = -\sin(x)\cdot D_x(x). The derivative of a sum of two or more functions is the sum of the derivatives of each function.

Final answer to the problem

$\cos\left(x^2-1\right)+x\left(-2x\right)\sin\left(x^2-1\right)$

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Function Plot

Plotting: $\cos\left(x^2-1\right)+x\left(-2x\right)\sin\left(x^2-1\right)$

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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
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

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