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How do you differentiate a^x?

The quick answer is that d/dx a^x = ln(a) * a^x. But why? Well, let's go through the steps so we can understand why the formula works. Firstly, a^x can be written as (e^(ln(a)))^x because e^(ln(z)) = z as th...
KM
Answered by Kian M. • Maths tutor
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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
9737 Views

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...
SM
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...
KH
Answered by Keir H. • Maths tutor
14667 Views

differentiate 2^x

y=2^x lny=xln2 y=e^(xln2)
MP
Answered by Mit P. • Maths tutor
6785 Views