Question

Find the derivative of the following by First principle of derivatives

1) ( x² + 3x^4)

Answer 1

Hey there!

$\frac{d}{dx} ( {x}^{2} + 3 {x}^{4} ) \\ = \frac{d}{dx} ( {x}^{2 } )+ \frac{d}{dx} (3 {x}^{4 } ) \\ = (2 \times {x}^{2 - 1} )+ (3 \times 4 \times {x}^{4 - 1} ) \\ = 2x + 12x ^{3}$

Formulas used :
1) d/dx ( u + v) = d/dx ( u) +d/dx(v)
2) d/dx( x^n) = nx^n-1
3) d/dx(Kx) = K d/dx(x)
Hope helped!