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Differentiate the function: y = sin(x^2)*ln(5x)

We are tasked with differentiating y = sin(x 2 ) ln(5x) This function is actually a product of the functions: sin(x 2 ) and ln(5x) Therefore the product rule will be required. First let's calculate the deriv...
TC
Answered by Thomas C. • Maths tutor
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How do you find the roots of a cubic equation?

Solving cubics is an interesting problem: while there is a formula which can find the roots of every cubic equation, it isn't taught and is not generally worth learning. Instead, exam questions will often gi...
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Answered by Sam M. • Maths tutor
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Let f(x) and g(x) be two odd functions defined for all real values of x. Given that s(x)=f(x)+g(x), prove that s(x) is also an odd function.

We recall that a function f(x) is said to be an odd function when f(-x)=-f(x) . We are told that f(x) and g(x) are odd functions, so we know from the above definition that: 1. f(-x)=-f(x) 2. g(-x)=-g(x) Solu...
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Answered by Keir H. • Maths tutor
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differentiate 2^x

y=2^x lny=xln2 y=e^(xln2)
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Answered by Mit P. • Maths tutor
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A pot of water is heated to 100C and then placed in a room at a temperature of 18C. After 5 minutes, the pan temperature falls by 20C. Find the temperature after 10minutes.

(The rate at which the temperature of a body falls is proportional to the difference between the body temperature and the room temperature) - this would be given in the question. This is a typical ordinary d...
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Answered by Asher C. • Maths tutor
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