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junior college 2 | H2 Maths
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Nelson Loo
Nelson Loo

junior college 2 chevron_right H2 Maths chevron_right Singapore

Does anyone knows how to differentiate?

Date Posted: 2 years ago
Views: 416
J
J
2 years ago
Implicit differentiation :

let y = f(x) = (4 + x)⁷⁺ˣ

Take ln on both sides,

ln y = ln(4 + x)⁷⁺ˣ
ln y = (7 + x) ln(4 + x)

Differentiate both sides with respect to x,

1/y dy/dx = (1) ln(4 + x) + (7 + x)(1/(4+x))

1/y dy/dx = ln(4 + x) + (7+x)/(4 + x)

dy/dx = y ( ln(4 + x) + (7+x)/(4 + x) )

dy/dx = (4 + x)⁷⁺ˣ ( ln(4 + x) + (7+x)/(4 + x) )

dy/dx = (4 + x)⁶⁺ˣ ( (4 + x) ln(4 + x) + 7 + x)


So, f'(x) = (4 + x)⁶⁺ˣ ( (4 + x) ln(4 + x) + 7 + x)

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J
J
2 years ago
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