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India
Class XI

Simple applications (using power rule only)

Interactive practice questions

Find the gradient of $f\left(x\right)=x^5-3x^4$f(x)=x53x4 at the point $\left(3,0\right)$(3,0).

Denote this gradient by $f'\left(3\right)$f(3).

Easy
1min

Consider the curve given by the function $f\left(x\right)=-\frac{27}{x^2}$f(x)=27x2.

Easy
2min

Find the gradient of $f\left(x\right)=\frac{11}{x}+\frac{10}{x^2}$f(x)=11x+10x2 at the point $\left(4,\frac{27}{8}\right)$(4,278).

Denote this gradient by $f'\left(4\right)$f(4).

Easy
2min

Find the gradient of $f\left(x\right)=\frac{6}{\sqrt{x}}$f(x)=6x at the point $\left(25,\frac{6}{5}\right)$(25,65).

Denote this gradient by $f'\left(25\right)$f(25).

Easy
2min
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Outcomes

11.C.LD.1

Derivative introduced as rate of change both as that of distance function and geometrically, intuitive idea of limit. Definition of derivative, relate it to slope of tangent of the curve, derivative of sum, difference, product and quotient of functions. Derivatives of polynomial and trigonometric functions.

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