Step-by-step Solution

Find the derivative using the product rule $\frac{d}{dx}\left(5e^{7x}\cos\left(9x\right)\right)$

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Final Answer

$35e^{7x}\cos\left(9x\right)-45e^{7x}\sin\left(9x\right)$
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Step-by-step Solution

Problem to solve:

$\frac{d}{dx}\left(5\cdot e^{7x}\cdot \cos\left(9x\right)\right)$

Choose the solving method

1

The derivative of a function multiplied by a constant ($5$) is equal to the constant times the derivative of the function

$5\frac{d}{dx}\left(e^{7x}\cos\left(9x\right)\right)$

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

$5\frac{d}{dx}\left(e^{7x}\cos\left(9x\right)\right)$

Unlock this full step-by-step solution!

Learn how to solve product rule of differentiation problems step by step online. Find the derivative using the product rule (d/dx)(5e^(7x)*cos(9x)). The derivative of a function multiplied by a constant (5) is equal to the constant times the derivative of the function. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=e^{7x} and g=\cos\left(9x\right). 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 the linear function times a constant, is equal to the constant.

Final Answer

$35e^{7x}\cos\left(9x\right)-45e^{7x}\sin\left(9x\right)$
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1
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5
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7
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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
|◻|
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

Tips on how to improve your answer:

$\frac{d}{dx}\left(5\cdot e^{7x}\cdot \cos\left(9x\right)\right)$

Related Formulas:

4. See formulas

Time to solve it:

~ 0.76 s