Definition of Gradient (Edexcel A-Level Mathematics): Flashcards

The gradient is $\frac{dy}{dx} = ke^{kx}$.

Differentiate to get $\frac{dy}{dx} = 18e^{3x}$ and substitute.

$y' = 18e^{3x}$, apply chain rule for differentiation.

Differentiate, evaluate at $\ln(2)$, use point-slope form.

Point is $(\ln(2), 6)$ since $3e^{\ln(2)} = 3 \cdot 2 = 6$.

$y = 6x - 6\ln(2)$ after expansion and simplification.

It's the gradient of a tangent at a specific point.

Estimates depend heavily on the curve's quality.

Differentiate the function with respect to $x$.

Differentiate, substitute $x$, and apply point-slope form.