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How to differentiate e^x . sin(x)

e x sin(x) is a product of two functions: e x and sin(x). This means we can use the product rule. Let e x = u and sin(x) = v The differential of uv is u'v + v'u where u' and v' are the two functions differen...
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Answered by Brent W. • Maths tutor
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A bag contains only apple and oranges. The probability an apple is picked randomly is 1 in 5. The apple is returned, and five more apples are added to the bag. The probability of an apple being picked is now 1in 3. How many apples were there originally?

2 simultaneous unknown equations. Let x be the number of apples originally, and n the number of fruits in the bag in total originally. i) first scenario, where probability is 1/5, x/n = 1/5 5x= n ii) second ...
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Answered by Chloe L. • Maths tutor
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Using examples, describe and explain how erosion results in the formation of two coastal landforms.

Coastal erosional landforms are commonly found in high energy environments, where large waves, strong winds and tidal currents drive erosion. There are a number of different mechanisms which cause erosion, i...
JB
Answered by James B. • Geography tutor
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How do you structure a business long marker question?

As a history student, I was rarely intimidated by the thought of a big marker business question unlike the rest of my peers. However, as time progressed throughout my Alevel study I realised just how easy it...
JR
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Differentiate arcsin(2x) using the fact that 2x=sin(y)

Differentiate implicitly on both sides with respect to x to get: 2=cos(y) • (dy/dx). Divide by cos(y) on both sides to get: dy/dx=2/cos(y). Use the trigonometric identity cos^2(y)+sin^2(y)=1 rearranged to co...
LO
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