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Differentiate 2e^(3x^2+6x)

Subsitute in u = 3x^2 + 6x and use chain rule to get dy/dx = dx/du x dy/dx to get dy/dx = 2(6x+6)e^(3x^2 +6)
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Answered by Nasser C. • Maths tutor
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Suppose that 3=2/x(1)=x(1)+(2/x(2))=x(2)+(2/x(3))=x(3)+(2/x(4))+...Guess an expression, in terms of n, for x(n). Then, by induction or otherwise, prove the correctness of your guess.

We have 3=2/x 1 =x 1 +2/x 2 =x 2 +2/x 3 =x 3 +2/x 4 =.... How can we guess at a general expression? One way is to try and see one by looking at the first few terms and looking for a pattern. We can calculate...
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Answered by George C. • STEP tutor
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Given that the binomial expansion of (1+kx)^n begins 1+8x+16x^2+... a) find k and n b) for what x is this expansion valid?

a) We compare the expansion given to the standard binomial expansion (remembering the powers of k).(1+kx) n =1+n(kx)+(n(n-1)/2)(kx) 2 +...As this is true for all x (for which the expansion holds), we can com...
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Answered by George C. • Maths tutor
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Given that y=(sin4x)(sec3x), use the product rule to find dy/dx

First, recall the Product rule: f(x)=g(x)*h(x), f'(x)=h(x)*g'(x)+h'(x)*g(x)This reveals the next step, to find the derivatives of our two subsidiary functions(g and h) d/dx * (sin4x) = 4cos(4x) , and d/dx (s...
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Answered by Edward F. • Maths tutor
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What is the defining characteristic of Cubism?

A multifaceted and enigmatic style of modern art, Cubism is defined primarily by its break with art historical tradition. Launched by Picasso and Braque in the first decade of the twentieth-century in Paris,...
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