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

Derive the function e^(7x)cos(9x)*5 with respect to x

Answer

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

Step-by-step explanation

Problem

$\frac{d}{dx}\left(5\cdot e^{7x}\cdot \cos\left(9x\right)\right)$
1

Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=5e^{7x}$ and $g=\cos\left(9x\right)$

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

Unlock this step-by-step solution!

Answer

$35e^{7x}\cos\left(9x\right)-45e^{7x}\sin\left(9x\right)$
$\frac{d}{dx}\left(5\cdot e^{7x}\cdot \cos\left(9x\right)\right)$

Main topic:

Differential calculus

Used formulas:

2. See formulas

Time to solve it:

0.31 seconds