to grow / to wax
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to grow
To increase in size, height, or extent. Refers to living things such as people, animals, and plants.
Die Tomaten in unserem Garten wachsen dieses Jahr besonders gut.
The tomatoes in our garden are growing especially well this year.
There are two verbs 'wachsen'. The strong verb means 'to get bigger' (er wächst, er wuchs, er ist gewachsen). The weak verb means 'to treat with wax' (er wachst, er wachste, er hat gewachst). You can recognize the difference from the conjugation and the auxiliary verb.
Der Baum ist schnell gewachsen.
The tree grew quickly.
In the meanings 'to get bigger' or 'to increase', 'wachsen' always forms the perfect tense with the auxiliary verb 'sein'. This is because it describes a change of state or movement.
Meine Kinder sind im letzten Jahr so viel gewachsen!
My children grew so much last year!
The expression 'einer Sache gewachsen sein' means that one can handle a challenge. The thing or person that one is up to is always in the dative.
Ich bin dieser Aufgabe voll und ganz gewachsen.
I am fully up to this task.
When 'wachsen' describes an increase, it is often used with abstract nouns. Typical combinations are 'die Wirtschaft wächst' (the economy is growing), 'die Sorge wächst' (concern is growing), 'das Interesse wächst' (interest is growing), or 'der Druck wächst' (pressure is growing).
Mit jedem Tag wuchs ihre Hoffnung, ihn wiederzusehen.
With each day, her hope of seeing him again grew.
to develop
'sich entwickeln' and 'wachsen' can both describe a change over a longer period of time. 'wachsen' usually means that something becomes bigger or increases, for example a child, a plant, or a number. 'sich entwickeln' is broader: it can also mean that something changes, improves, becomes more mature, or becomes more complex. The words can be confused because both describe a process. If only size or quantity is important, 'wachsen' fits better. If the type of change is important, 'sich entwickeln' fits better.
Die Pflanze wächst schnell, weil sie genug Licht und Wasser bekommt.
The plant is growing quickly because it gets enough light and water.
Im Laufe des Projekts entwickelt sich aus der einfachen Idee ein guter Plan.
Over the course of the project, the simple idea develops into a good plan.