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Core 3 Differentiation: If y = (3x^2 + 2x + 5)^10, find its derivative, dy/dx. Hint: Use the chain rule.

The function y = (3x 2 +2x+5) 10 is an example of a "function within a function", which means the thing in the brackets is a function itself, and it's being raised to the power of 10. This is a str...
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Find X log(x)=4 Base 10

Log base 10log(x)=4 ~ 10 4 =xx=10000
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Solve the simultaneous equations y+4x+1 = 0 and y^2+5x^2+2x = 0

x = -1/3 and y = 1/3 or x = -1/7 and y = -3/7
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Answered by Mustafa Q. • Maths tutor
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Prove that 1 + tan^2 x = sec^2 x

We know that tan x = sin x/cos x and so tan 2 x = sin 2 x/cos 2 x. We also know that sin 2 x + cos 2 x = 1 because this is a Pythagorean identity. We can rewrite the left hand side as (cos 2 x + sin 2 x)/cos...
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Answered by Eleanor F. • Maths tutor
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Integrate 2x^2 + 4

When we integrate, we raise the power by one and divide the term by the new power. So let's break the question down term by term. When integrating 2x 2 we raise the power by 1 to get 2x 3 . We then divide 2x...
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Answered by Eleanor F. • Maths tutor
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