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junior college 2 | H2 Maths
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Does anyone knows how to differentiate?
Date Posted: 3 years ago
Views: 459
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)
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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