# Find dydx, if y = (3x2+x+5)45 - Mathematics and Statistics

Sum

Find ("d"y)/("d"x), if y = root(5)((3x^2 + 8x + 5)^4

#### Solution

y = root(5)((3x^2 + 8x + 5)^4

y = (3x^2 + 8x + 5)^(4/5)

Differentiating both sides w.r.t. x, we get

("d"y)/("d"x) = "d"/("d"x) [(3x^2 + 8x + 5)^(4/5)]

= 4/5(3x^2 + 8x + 5)^(-1/5)*"d"/("d"x)(3x^2 + 8x + 5)

= 4/5(3x^2 + 8x + 5)^(-1/5)*[3(2x) + 8 + 0]

∴ ("d"y)/("d"x) = 4/5(3x^2 + 8x + 5)^(1/5)*(6x + 8)

Concept: Derivatives of Composite Functions - Chain Rule
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