Question

1a Differentiate the following functions.

 

𝑦=5𝑥3−3𝑥2+5𝑥2−7 𝑤.𝑟.𝑡.𝑥

 

𝑣=5𝑒2𝑦−𝑒−3𝑦 𝑤.𝑟.𝑡.𝑦

 

𝑦=4𝑠𝑖𝑛2𝜃−2𝑐𝑜𝑠4𝜃 𝑤.𝑟.𝑡.𝜃

Answer 1

Solutions:-

(1) $\boxed{\frac{dy}{dx} = 15x^2 + 10x}$

(2) $\frac{dv}{dy} = 5e^2 (-e)y^{-e-1 \space }-3$

$\boxed{\frac{dv}{dy} = -5e^3y^{-e-1 \space }-3}$

(3) $\boxed{\frac{dy}{d \theta} = 8cos(2\theta) + 8sin(4\theta)}$