How do you differentiate # y =cos(3x+7) # using the chain rule?

1 Answer
Shail P.
Jun 21, 2016

#-3sin(3x+7)#

Explanation:

The chain rule: #d/dx[f(g(x))] = f'(g(x)) * g'(x)#

Essentially, you take the derivative of whatever is on the outside like normal then multiply it by whats on the inside of the trig function.

The derivative of #cos(x)# is #-sin(x)#
so taking the derivative of the outside gives us: #-sin(3x + 7)#
then we take the derivative of the inside: #d/dx[3x+7] = 3#

The derivative of the inside is then multiplied by our first derivative:

# -sin(3x+7) * 3 = -3sin(3x+7)#

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