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4.01 Differentiation Review

Interactive practice questions

Find the derivative of $y=x^6+x^{\frac{1}{5}}$y=x6+x15.

Give your answer with positive indices.

Easy
1min

Differentiate $y=18x\sqrt{x}$y=18xx. Leave your answer in surd form.

Easy
2min

Find the derivative of $y=x^{\frac{1}{2}}+8x^{\frac{3}{4}}$y=x12+8x34.

Easy
1min

Consider the function $f\left(x\right)=\left(5x^3-4x^2+3x-5\right)^7$f(x)=(5x34x2+3x5)7.

Redefine the function as composite functions $f\left(u\right)$f(u) and $u\left(x\right)$u(x), where $u\left(x\right)$u(x) is a polynomial.

Easy
1min
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Outcomes

MA12-3

applies calculus techniques to model and solve problems

MA12-6

applies appropriate differentiation methods to solve problems

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