Y = 2x^3sinx - 3xcosx Find the derivative of the equation?

Answer 1

#dy/dx=(2x^3-3)cosx+(6x^2+3x)sinx#

Each term has to be differentiated using the #color(blue)"product rule"#
#"Given "f(x)=g(x).h(x)" then"#
#color(red)(bar(ul(|color(white)(2/2)color(black)(f'(x)=g(x)h'(x)+h(x)g'(x))color(white)(2/2)|)))larr" product rule"#
#color(magenta)"First term"#
#"for "f(x)= 2x^3sinx#
#"here "g(x)=2x^3rArrg'(x)=6x^2#
#h(x)=sinxrArrh'(x)=cosx#
#rArrf'(x)=2x^3(cosx)+6x^2(sinx)to(1)#
#color(magenta)"Second term"#
#f(x)=3xcosx#
#"here "g(x)=3xrArrg'(x)=3#
#h(x)=cosxrArrh'(x)=-sinx#
#rArrf'(x)=3x(-sinx)+3cosxto(2)#
#"Combining differentiated terms, that is " (1)-(2)#
#dy/dx=2x^3cosx+6x^2sinx+3xsinx-3cosx#
.>#rArrdy/dx=(2x^3-3)cosx+(6x^2+3x)sinx#
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Answer 2

To find the derivative of the equation Y = 2x^3sinx - 3xcosx, you can use the product rule and the chain rule.

The derivative of Y with respect to x, denoted as Y', is given by: Y' = (6x^2sinx + 2x^3cosx) - (3cosx + 3xsinx)

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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.

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.

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.

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.

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