How do you differentiate #cos(x^4)-2sinx#?

Answer 1

#-4x^3sin(x^4)-2cosx#

Using #color(blue)"standard derivatives"#

#color(orange)"Reminder " color(red)(bar(ul(|color(white)(2/2)color(black)(d/dx(sinx)=cosx,d/dx(cosx)=-sinx)color(white)(2/2)|)))#

differentiate the first term using the #color(blue)"chain rule"#

#• d/dx[cos(f(x))]=-sin(f(x))xxf'(x)#

#rArrd/dx[cos(x^4)-2sinx]#

#=-sin(x^4)xxd/dx(x^4)-2cosx#

#=-4x^3sin(x^4)-2cosx#

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Answer 2

Emily Ammerman

To differentiate cos(x^4) - 2sin(x) with respect to x, apply the chain rule for the differentiation of cos(x^4) and the differentiation of -2sin(x).

The derivative of cos(x^4) is -4x^3sin(x^4), and the derivative of -2sin(x) is -2cos(x).

So, the derivative of cos(x^4) - 2sin(x) with respect to x is -4x^3sin(x^4) - 2cos(x).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.